General Physics
Objective Question
Q.1 The fundamental unit which
has same power in the dimensional formula of surface tension and viscosity is :
(a) Mass (b) Length (c) Time (d) None
Q.2 Indicate which pairs of physical quantities given below has not the
same units and dimensions :
(a)
Momentum and impulse
(b)
Torque and angular momentum
(c)
Acceleration and gravitational field strength
(d)
Pressure and modulus of elasticity
Q.3 The dimensions of pressure are :
(a) [MLT-2] (b) [ML-1T2] (c) [ML-1T-2] (d) [MLT2]
Q.4 The dimensions of torque are
:
(a) [M L2 T-2] (b) [M L
T-2] (c) [M L-1 T--2] (d) [ML-2
T-2]
(a) [M0L2T-2] (b) [ML2T-1] (c) [MLT-1] (d) [ML2T-2]
Q.6 Planck’s constant has the
dimensions of :
(a) Energy (b) Momentum (c) Frequency
(d) Angular
momentum
Q.7 The dimensional formula for
Planck’s constant is :
(a) [ML2T-1] (b) [ML2T3] (c) [ML-1T-2] (d) [MLT-2]
Q.8 The dimensions of
gravitational constant G are :
(a) [MLT-2] (b) [ML3T-2] (c) [M-1L3T-2] (d) [M-1LT-2]
Q.9 The dimensional formula for
modulus of rigidity is :
(a) [ML-1T-1] (b) [ML-2T2] (c) [MLT-1] (d) [ML-1T-2]
Q.10 Turpentine oil is flowing through a tube of length l and
radius r. The pressure difference between the two ends of the tube is p; the
viscosity of the oil is given by :
h = p (r2 – x2)/4nl
where v is the
velocity of oil at a distance x from the axis of the tube. From this relation,
the dimensions of viscosity h are :
(a) [M0L0T0] (b) [MLT-1]
(c) [ML2T-2] (d) [ML-1T-1]
Q.11 The velocity n of a point at time t is given by :
n = at + b/ (t + c)
The dimensions of a, b
and c are respectively :
(a) L2; T and LT2 (b) LT2; LT and L
(c) LT-2; L and T (d) L; LT and T2
Q.12 The time dependence of a physical quantity p is given by P = P0
exp (-at2) [where a is a constant and t is time]. The constant a:
(a) is dimensions [T2] (b) has dimensions [T-2] (c) is dimensions (d) is dimensions of p
Q.13 The
velocity of water waves may depends on their wavelength l, the density of water r and the acceleration due to gravity g. The
method of dimensions gives the relation between these quantities as :
(c) V2
µ glr (d) V2 µ g-1 l-3
Q.14 The
time period T of a small drop of liquid (due to surface tension) depends on
density r, radius r and surface
tension S. The relation is :
(a) T µ (rr3/S)1/2 (b) T µ rrS
(c) T µ rr/S (d) T µ (S/rr)
Q.15 P
represents radiation pressure, c represents speed of light and S represents
radiation energy striking unit area per sec. The non zero integers x, y and z
such that PxSycz is dimensionless are :
(a) x = 1, y =1, z = 1 (b) x = -1, y =1, z = 1
(c) x = 1, y =-1, z = 1 (d) x = 1, y =1, z = 1
Q.16 The measured mass and volume of a body are 23.42 g and 4.9 cm3
respectively with possible error 0.01 g and 0.1 cm3. The maximum
error in density is nearly
(a) 0.2% (b) 2% (c) 5%
(d) 10%
Q.17 The
least count of a stop watch is 0.2 second. The time of 20 oscillations of a
pendulum is measured to be 25 second. The percentage error in the measurement
of time will be
(a) 8% (b) 1.8% (c) 0.8%
(d) 0.1%
Q.18 A
student measures quantities a,b and c and then calculates S by the formula S =
ab2/c3. If the errors in a,b,c are 1%, 3% and 2%
respectively, the maximum error in S can be :
(a) 13% (b) 7% (c) 4% (d) 1%
Q.19 The
percentage errors in the measurement of mass and length of the edge of a cube
are 3% and 2% respectively. The maximum percentage errors in the density would
be :
(a) 1% (b) 5% (c) 9% (d) 11%
Q.20 The
pressure on a square plate is measured by measuring the force on the plate and
the length of the side of the plate. The errors in the measurement of force and
length are 4% and 2% respectively. The maximum error in the value of the
pressure would be
(a) 1% (b) 2% (c) 6% (d) 8%
Q.21 Four
persons measure the thickness of a paper and express it in the following way.
Which measurement is maximum accurate?
(a) 3.00 ´ 10-4 m (b) 30 ´ 10-3 cm
(c) 3 ´ 10-2 cm (d) 0.030 cm.
Q.22 The
length and breadth of a metal sheet are 3.124m and 3.002 m respectively. The
area of this sheet up to four correct significant figures is
(a) 9.3m2 (b) 9.378m2
(c) 9.3782m2 (d) 9.378248m2.
Q.23 Which of
the following measurements is most significant?
(a) 0.003 mm (b) 3.00
mm (c) 30.00 mm (d) 3.0 mm
Q.24 A vectors A points vertically upwards and B
points toward north. The vectors produced A ´ B is :
(a)
along west (b) along east
(c)
zero (d) vertically
downwards
Q.25 Which of the following physical quantities are
represented by polar vectors?
(a) Displacement (b) Angular Velocity
(c) Angular momentum (d) Torque
Q.26 The
flight of a bird can be example of :
(a) dot product of vectors (b) cross
product of vectors
(c) composition of vectors (d) Triangle
law of vector addition
Q.27 The vectors A and B are such thatú A + Bú =ú A – Bú
then the angle between the two vectors A and B will be
(a) 0° (b) 60° (c) 90° (d) 180°
Q.28 Two vectors A and B are such
that A + B = C and
A2 + B2 = C2. If q is the angle between positive directions A and
B then mark the correct alternative :
(a) q
= 0° (b) q = p/2 (c) q = 2p/3 (d) q = p
Q.29 A + B = C, the angle
between A and B is 120°
and A = B. If A + B + C = 0°. Then what is the angle between A and B?
(a) 30° (b) 60° (c) 120° (d) 150°
Q.30 If | P | = | Q | and the angle between P and Q is neither 0° nor 180°, then what is the angle between P + Q and P – Q?
(a) 0° (b) 30° (c) 60° (d) 90°
Answer Sheet
General Physics
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Kinematics
DISTANCE, DISPLACEMENT AND
VELOCITY,ACCLERATED MOTION
Q.1 A ball is thrown vertically
upwards from the ground G with a speed u. It reaches a point B at a height h
(lower than the maximum height) after time t1. It return to the
ground after time t2 from the instant it was at B during the upward
journey. Then t1t2 is equal to :
(a) 2h/g (b) h/g (c) h/2g (d) h/4g
Q.2 A ball is dropped
from the top of the tower of height h. It covers a distance of h/2 in the last
second of its motion. How long does the ball remain in air? (Take g = 10 ms-2)
(a) Ö2s (b) (2 ±Ö2)s (c) 2s
(d) none
of these
Q.
3 A bus is
moving with a velocity 10 ms-1 on a straight road. A scooterist
wishes to cover-take the bus in 100 s. If the bust is a distance of 1 km from
the scooterist, with what velocity should the scooterist chase the bus?
(a) 50 ms-1 (b) 40 ms-1 (c) 30 ms-1 (d) 20 ms-1
Q.4 A car is
moving eastwards with velocity 10 m/s. In 20 sec, the velocity changes to 10
m/s northwards. The average acceleration in this time :
(a) 1/Ö2
ms-2 towards N-W (b) 1/Ö2
ms-2 towards N-E
(c) ½
ms-2 towards N-W (d) ½
ms-2 towards N-E
Q.5 A
body starts from rest with a uniform acceleration of 2 m/s2 for 10
sec, it moves with constant speed for 30 sec then decelerates by 4 m/s2
to zero. What is the distance covered by the body?
(a) 750 m (b) 850 m (c) 600
m
(d) none
of these
Q.6 A
body dropped from a height h with an initial speed zero reaches the ground with
a velocity of 3 km/h. Another body of the same mass was dropped from the same
height h with an initial speed 4 km/h, will reach the ground with a velocity of
:
(a) 3 km/h (b) 4 km/h (c) 5 km/h (d) 12 km/h
Q.7 A parachutist after
bailing out falls 50 m without friction when parachute opens, it decelerates at
2 m/s2. He reaches the ground with a speed of 3 m/s. At what height, did he bail out?
(a) 293 m (b) 111m (c) 91
m (d) 182
m
Q.8 A car covers 1/3
distance with speed 20 km/hr and 2/3 with 60 km/hr. Average speed is :
(a) 40 km/hr (b) 50Ö2
km/hr
(c) 36
km/hr (d) 48 km/hr.
Q.9 A particle is
thrown vertically upwards. Find the velocity so that it covers same distance in
5th and 6th seconds :
(a) 48 m/s (b) 14 m/s (c) 49 m/s (d) 7 m/s.
Q.10 From the top of a
tower, a particle is thrown vertically downwards with a velocity of 10 m/s. The
ratio of the distance covered by it in the 3rd and 2nd
seconds of the motion is :
(a) 5 : 7 (b) 7
: 5 (c) 3
: 6 (d) 6
: 3.
Q.11 A
ball is thrown from height h and another from 2h. The ratio of time taken by
the two balls to reach ground is :
(a) 1: Ö2 (b) Ö2
: 1 (c) 2
: 1 (d) 1
: 2.
Q.12 Two bodies A (off
mass 1 kg) and B (of mass 3 kg) are dropped from height of 16 m and 25 m
respectively. The ratio of the time taken by them to reach the ground is :
(a) 4/5 (b) 5/4 (c) 12/5 (d) 5/12.
(a) zero (b) 1/Ö2
m s-2 towards north-west
(c) 1/Ö2
m s-2 towards north-east (d) ½
m s-2 towards north.
Q.14 A-Train covers one half of its journey between two
stations with speed v1 and
the remaining half with speed v2.
The average speed for the whole journey is
(a) v1+v2/2 (b) 2 v1v2 / v1+v2 (c) Ö v1v2 (d) Ö v1/v2
Q.15 A 150 m long train is moving north at a speed of
20m/s. A bird flying south at a speed of 5m/s cross the train. What is the time
taken by the bird to cross the train
(a) 30s (b) 10s (c) 7.5s (d) 6s
Q.16 From a 20 m high tower one ball is thrown upwards
with speed of 10m/s and another is thrown vertically downwards at the same
speed simultaneously. The time difference of their reaching the ground will
be (Take g = 10ms-2)
(a) 12s (b) 6s (c) 2s (d) 1s
Q.17 A particle is projected vertically upwards. It
attains a height h after 2 seconds
and again after 10 seconds. The speed of the particle at the height h is numerically equal to
(a) g (b) 2g (c) 4g (d) 6g
Q.18 Two objects begin free fall from rest from the same
height with a time gap of 1s. How long after the first object begins to fall
will the two bodies be 10m apart.
(a) 3.5s (b) 2s (c) 0.5s (d) 1.5s
Q.19 If the
speed of a truck is reduced to 1/3 of its original value, the minimum distance
required to stop will be
(a) same
as before (b) 1/3
of its original value
(c) 1/9
of its original value (d) 2/3
of its original value
Q.20 The magnitude of average velocity
is equal to the average speed when a particle moves :
(a) on
a curved path (b) in
the same direction
(c) with
constant acceleration (d) with
constant retardation
Q.21 If
a particle moves with a constant velocity :
(a) its
acceleration is positive (b) its
acceleration is negative
(c) its
acceleration is zero (d) its
speed is zero
Q.22 A particle
moving in a straight line cover half the distance with speed of 3 m/s. the
other half of the distance is covered in two equal time intervals with speed of
4.5m/s and 7.5 m/s respectively. The average speed of the particle during this
motion is :
(a) 4 m/s (b) 5 m/s (c) 5.5 m/s (d) 4.8 m/s
Q.23 A ball is released from the top of a tower
of height h meters. It takes T seconds to reach the ground. What is the
position of the ball at T/3 second ?
(a) 8h/9 meters from the ground (b) 7h/9 meters from
the ground
(c) h/9 meters from the ground (d) 17h/18 meters from the ground
Q.24 If
a train traveling at 72 km/h is to be brought to rest in a distance of 200m,
then its retardation should be :
(a) 20 m/s2 (b) 2 m/s2 (c) 10 m/s2 (d) 1 m/s2
Q.25 A body travels 200 cm in the
first two seconds and 220 cm in the next 4 sec with deceleration. The velocity
of the body at the end of the 7th second is :
(a) 5 cm/s (b) 10 cm/s (c) 15 cm/s (d) 20 cm/s
Q.26 A car moving with a
speed of 40 km/hr, can be stopped by applying brakes after at least 2m. If the
same car is moving with a speed of 80 km/hr, what is the minimum stopping
distance?
(a) 2 m (b) 4 m (c) 6 m (d) 8 m.
Q.27 An electron of mass
me, initially at rest, moves through a certain distance in a uniform
electric field in time t1. A proton of mass mp, also
initially at rest, takes time t2 to move through an equal distance
in this uniform electric field. Neglecting the effect of gravity, the ration t2/t1
is nearly equal to :
(a) 1 (b) (mp/me)1/2 (c) (me/mp)1/2 (d) 1836
Q.28 A particle is
dropped vertically from rest, from a height. The time taken by it to fall
through successive distance of 1 km each will then be :
(a) all equal, being equal to Ö2/g
second
(b)
in the ratio of the square roots of
the integers 1, 2 3, . . .
(c)
in the ratio of the difference in the
square roots of the integers, i.e., Ö1, (Ö2 - Ö1), (Ö3
- Ö2),
(Ö4
- Ö3),
. . .
(d)
in the ratio of the reciprocal of the
square roots of the integers, i.e, 1/Ö1 , 1/Ö2 , 1/Ö3 , .
. .
Q.29 An object accelerates from rest to a
velocity 27.5 m/s in 10 sec, then find distance covered by next 10 sec:
(a) 550 m (b) 137.5 m (c) 412.5 m (d) 275 m.
Q.30 A body falls freely
from rest. It covers as much distance in the last second of its motion as
covered in the first three second. The body has fallen for a time of :
(a) 3 s (b) 5 s (c) 7 s (d) 9 s
Answer Sheet
DISTANCE, DISPLACEMENT AND
VELOCITY,ACCLERATED MOTION
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Graph
& Problems on Integration and Differentiation
Q.1 A particle moves along x-axis in such a way that its
coordinate x varies with time t according to the expression
x = 2 – 5t + 6t2
The initial velocity of the particle is (a) - 5m/s (b) -3 m/s (c) 3 m/s (d) 6 m/s
Q.2 A particle
starts from rest and travels in a straight line with an acceleration which
varies with time t as follows
a
= 6 – 2 t
The distance traveled by the particle in 3s is (a) 9 m (b) 12 m (c) 15 m (d) 18 m
Q.3 A bird
flies in straight line for 4s with a velocity n = (2t - 4) m/s. What is the distance covered by the
bird in returning to the place from where it started its journey? (a) 0 (b) 8 m (c) 4 m (d) 2 m
Q.4 A particle
starts from rest at the origin and moves along X-axis with acceleration
The time after which the particle arrives at the
origin is
(a) 6 s (b) 18 s (c) 12 s (d) 4 s
Q.5 The
position x of a particle varies with time (t) as x = at2 – bt3.
The acceleration at time t of the particle will be equal to zero, where t is
equal to :
(a) 2a/3b (b) a/b (c) a/3b (d) zero
Q.6 The displacement s of a particle is proportional to
the first power of time t, i.e., s µ t, then the acceleration of the particle is :
(a) infinite
(b) zero
(c) a
small finite value (d) a large finite value
Q.7 The displacement s of a particle is proportional to
the second power of time t, i.e., s µ t2, then the initial velocity of the
particle is :
(a) infinite
(b) zero
(c) positive
finite value (d) negative finite value
Q.8 The distance traveled by a particle is directly
proportional to t1/2, where t = time elapsed. What is the nature of
motion?
(a) Increasing
acceleration (b) Decreasing acceleration
(c) Increasing
retardation (d) Decreasing retardation
Q.9 The displacement of a body is given by 4s = M + 2Nt4,
where M and N are constants. The velocity of the body at any instant is :
(a) M
+ 2Nt4/4 (b) 2N (c) M + 2 N/4 (d) 2Nt3
Q.10 The
acceleration of particle, starting from rest, varies with time according to the
relation :
A = -sw2 sin wt
The displacement of this particle at
a time t will be :
(a) s sin wt (b) sw cos wt (c) sw sin wt(d) ½ (sw2 sin wt)t2
Q.11 If x denotes
displacement in time t and x = a cos t, then acceleration is :
(a) a cos t (b) - a cos t (c) a
sin t (d) -a sin t
Q.12 The relation
between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is :
(a) -2av3 (b) 2bv3 (c) -2abv3 (d) 2b3v3
(a) 9 m (b) 16 m (c) 27
m (d) 36 m
Q.14 A
particle moves along a straight line such that its displacement at any time t
is given by
S
= (t3 – 3t2 + 2)m
The displacement when the
acceleration becomes zero is :
(a) 0 m (b) 2 m (c) 3 m (d) -2 m
Q.15 A point moves in a straight line so that its
displacement x m at time t sec is given by x2 = 1 + t2.
Its acceleration in m/sec2 at a time t sec is
(a) 1/x3 (b) -t/x3
(c) 1/x – t2/x3 (d) 1/x – 1/x3
Q.16 A body is
moved along a straight line by a machine delivering constant power. The distance
moved by the body in time t is proportional to :
(a) t1/2 (b) t3/4 (c) t3/2 (d) t2
Q.17 The displacement of a particle after time t is given
by x = (k/b2)(1 –e-bt), where b is a constant. What is
the acceleration of the particle?
(a) ke-bt (b) -ke-bt (c) k/b2e-bt (d) -k/b2e-bt
Q.18 The velocity v and displacement r of a body are
related as v2 = kr, where k is a constant. What will be the velocity
after 1 second? Given that the displacement is zero at t = 0 :
(a) Ök r (b) k r3/2
(c) k/2r0 (d) data is not sufficient
Q.19 A particle’s position as a function of time is
described as y (t) = 2t2 + 3t + 4. What is the average velocity of
the particle from t = 0 to t = 3 sec?
(a) 3 m/s (b) 6 m/s (c) 9
m/s (d) 12 m/s
Q.20 The displacement x of a particle moving in one
dimension under the action of constant force is related to time t by the
equation t = Öx + 3, where x is in metres and t is in seconds. Find the displacement
of the particle when its velocity is zero.
(a) zero (b) 12 m (c) 6
m (d) 18 m
Q.21 A travelling wave in a stretched string is described
by the equation y =A sin (kx -w t) The maximum particle velocity is
(a) Aw (b) w/k (c) dw/dt (d) x/t
Q.22 The x and y coordinates of a particle at any time t are given by
:
x = 7t + 4t2
and y
= 5t
Where x and y are in m and t in s.
The acceleration of the particle at 5s
is :
(a) zero (b) 8 m/s2 (c) 20
m/s2 (d) 40 m/s2
Q.23 The position vector of a particle is given by r = r0
(1 - at)t, where t is the time and a as well as r0 are constants.
After what time the particle returns to the starting point ?
(a) a (b) 1/a (c) a2 (d) 1/a2
Q.24 The acceleration of a particle varies with time as a =
bt + c, where b and c are constant. What will be the velocity of the particle
which starts from rest after the time t?
(a) bt + 1/2ct2 (b) ct + ½ bt2 (c) bt + ct2 (d) ct + bt2
Q.25 A
body is moving according to the equation :
x = at + bt2
– ct3
where x = displacement and a, b and
c are constants. The acceleration of the body is :
(a) a + 2bt (b) 2b + 6ct
(c) 2b – 6ct (d) 3b – 6ct2
Answer Sheet
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(c)
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PROJECTILE MOTION
Q.1 An
object is thrown along a direction inclined at an angle of 45° with the
horizontal. The horizontal range of the particle is equal to
(a) vertical
height (b) twice
the vertical height
(c) thrice
the vertical height (d) four
the vertical height
Q.2 The
greatest distance to which a man can throw a stone is a. The greatest height to which he can throw it will be
(a) a (b) a/2 (c) 2/ a (d) a/3
Q.3 Two
bodies are projected from the same point with the same speed but in different
directions so as to have the same range. The ratio of their times of flight are
(a) 1:1 (b) 1: cos q (c) 1: sin q (d) 1: cot q
Q.4 The
range of projectile which is launched at an angle of 15° with the
horizontal is 1.5km. What is the range of the projectile if it is projected at
an angle of 45° to the
horizontal?
(a) 1.5km (b) 3.0km (c) 6.0km (d) 0.75km
Q.5 A
man has two spheres A and B. He is standing at the top of a tower.
He gently drops the sphere A
vertically downwards and throws the sphere B
horizontally at the same time. Which of the following is the correct statement?
(a) both
the sphere will reach the ground simultaneously
(b) sphere
A will reach the ground earlier
(c) sphere
B will reach the ground earlier
(d) the
question is incomplete because the masses of the sphere are not given
Q.6 The
range of projectile is 24m and the maximum height reached is 8m. The initial
velocity and angle of projection are
(a) 6Ög , sin-1(0.8) (b) 5Ög , sin-1(0.6)
(c) 5Ög , sin-1(0.8) (d) 4Ög , sin-1(0.6)
Q.7 A
particle is projected with the speed of 10Ö5m/s at an angle of 60° from the horizontal, the velocity in m/s of the projectile when
it reaches the height of 10m is (Take g=9.8m/s)
(a) 4Ö19 (b) Ö179 (c) 15 (d) 5Ö15
*Q.8 A
lift is moving vertically upwards. At the instant when its velocity is v and downward acceleration is a (<g), a stone is projected from a point on its floor at an angle q with the
horizontal. The trajectory of the stone is
(a)
a parabola in the lift frame (b) a parabola in the ground frame
(c) a
straight line in the lift frame (d) a
straight line in the ground frame
Q.9 A particle is projected with a
velocity of 19.6m/s at an angle of 30° with the horizontal. It will move at right angles to its initial
directions of motion after a time of
(a) 2s (b) 6s (c) 4s (d) 8s
Q.10 A
particle of mass m is projected from
a point A at an angle of 45° with the
horizontal with a speed v. If the
time taken to reach the highest point B
is t, What is the change in its
velocity from its departure at A to
its arrival at B?
(a) Ö2v (b) v/Ö2 (c) gt (d) ½
gt2
Q.11 A
projectile of mass m is fired with
the velocity v from ground at an
angle of 45° with
horizontal. Neglecting air resistance, the magnitude of change in momentum
between leaving and arriving at the ground is
(a) zero (b) ½ mv (c) Ö2 mv (d) 2mv
Q.12 A
shell is fired a cannon with a velocity v
at an angle q with the horizontal direction. At the
highest point in its path it explodes into two pieces of equal mass. One of the
pieces retraces its path to the canon and the speed of the other piece
immediately after the explosion is
(a) 3v cos q (b) 2v cosq (c) 3/2 v cos q (d) Ö3/2 v cosq
Q.13 A body of mass 1kg is thrown from a point A with a velocity 20m/s at an angle 45° with the horizontal. If the highest point attained by it is B, calculate the work done by the
gravity during its journey from A to B. (g=
take 10 m/s2)
(a) 200J (b) –200J (c) –100J (d) 100J
Q.14 A body of mass
1kg is thrown with a velocity 40m/s at an angle of 30° with the
horizontal. What is the change in its momentum during the interval 1.0s to 3.0s
(Take g = 10m,/s2)
(a) –20kg ms-1 (b) 40kg ms-1 (c) 0 (d) –40 kg ms-1
Q.15 A
body of mass 1kg is thrown with a velocity of 40m/s at an angle of 30° with the horizontal. Calculate the work done by the gravity during the
interval of 1.0s to 3.0s (Take g = 10m,/s2)
(a) 800J (b) 400J (c) –800J (d) 0
*Q.16 In
case of projectile motion of two projectiles A and B are projected with the
same speed at angles 15° and 75° respectively to
the horizontal, then
(a) HA
> HB (b) HA < HB (c) TA >
TB (d) TA
< TB
Q.17 A
projectile of mass m is fired with velocity v pass a point A making an angle 45° with the
horizontal. Neglecting air resistance, the magnitude of change in momentum
between the starting point A and the arriving point B is
(a) Ö2 mv (b) 2 mv (c) (1
- 2) m v (d) (mv)1/2
Q.18 A
particle is thrown with a speed u at an angle q with the horizontal. When the particle makes an angle f with the
horizontal, its speed changes to v, which is equal to
(a) u
cos q (b) u
cos q cos f (c) u cos q sec f (d) u sec q cos f
Q.19 A
cannon ball has the same range R on a horizontal plane for two angles of
projection. If h1 and h2 are the greatest heights in the
two paths for which this possible, then
(a) R
= (h1h2)1/4 (b) R
= Öh1h2 (c) R = 4 Öh1h2 (d) R = Öh1h2
Q.
(a) 1:3 (b) 3: 1 (c) Ö3: Ö2 (d) 1: Ö3
Q.21 A particle is projected at an elevation
tan-1 (5/3) from a point O. The ratio of the range on the horizontal plane
through O to the greatest height ascended above O is
(a) 2 (b) 2.4 (c) 0.4 (d) 1.5
Q.22 After one second the velocity of a
projectile makes an angle of 45° with the
horizontal. After another one second it is traveling horizontally. The
magnitude of its initial velocity and angle of projection are (g = 10 m/sec2)
(a) 14.62
ms-1, tan-1 (2) (b) 22.36
ms-1, tan-1 (2)
(c) 14.62
ms-1, 60° (d) 22.36
ms-1, 60°
Q.23 A particle is projected from the ground with
an initial speed of u at an angle q with horizontal. The average velocity of the particle between its
point of projection and highest point of trajectory is
(a) u cos q (b) u/2
Ö1 + cos2
q
(c) u/2
Ö1 + 2cos2
q (d) u/2 Ö1 + 3 cos2
q
Q.24 The maximum height attained by a projectile
is increased by 5%. Keeping the angle of projection constant, what is
percentage increase in the horizontal range?
(a) 5% (b) 10% (c) 15% (d) 20%
Q.25 The maximum height attained by a projectile
is increased by 10%. Keeping the angle of projection constant, what is
percentage increase in the time of flight?
(a) 5% (b) 10% (c) 20% (d) 40%
Q.26 The equation of motion of a projectile is : y = 12x – 3/4 x2
The
horizontal component of velocity is 3ms-1. Given that g = 10 ms-2,
what is the range of the projectile?
(a) 12.4m (b) 21.6m (c) 30.6 m (d) 36.0 m
Q.27 A body is projected is up a smooth inclined plane
with velocity V from the point A as shown in the figure. The angle of
inclination is 45° and the top is connected to
a well of diameter 40 m. If the body just manages to cross the well, what is
the value of V? Length of inclined plane is 20Ö2 m.
(a) 40 ms-1 (b) 40Ö2 ms-1 (c) 20 ms-1 (d) 20Ö2 ms-1
Q.28 Galileo writes that for angles of projection of a
projectile at angles (45 + a) and (45 - a), the horizontal ranges described by the
projectile are in the ratio of :
(a) 2 : 1 (b) 1 : 2 (c) 1 : 1 (d) 2
: 3
Q.29 A projectile is fired from level ground at an angle q above the horizontal. The elevation angle f of the highest point as seen from the launch
point is related to q by the relation :
(a) tan f =1/4 tan q (b) tan f = tan q
(c) tan f = 1/2 tan q (d) tan f = 2 tan q
Q.30 Which of the
following is the essential characteristic of a projectile?
(a)
Initial velocity inclined to the horizontal (b) Zero velocity at the highest point
(b)
Constant acceleration perpendicular to the velocity
(c)
None of the above
ANSWERSHEET
Projectile Motion
1.
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(d)
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2.
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(b)
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3.
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(d)
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4.
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(b)
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5.
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(a)
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6.
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(c)
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7.
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(a)
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8.
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(a), (b)
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9.
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(c)
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10.
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(c)
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11.
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(c)
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12.
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(a)
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13.
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(c)
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14.
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(a)
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15.
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(d)
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16.
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(b), (d)
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17.
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(a)
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18.
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(c)
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19.
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(c)
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20
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(d)
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21.
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(b)
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22.
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(b)
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23.
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(d)
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24.
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(a)
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25.
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(a)
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26.
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(b)
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27.
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(d)
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28.
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(c)
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29.
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(c)
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30.
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(d)
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