ACE SCIENCE ACADEMY

Physics
Total Questions : 45 Total Marks : 180
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30-Oct-2020
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i) All Questions are compulsory
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Unit Test
• Motion in One Dimension
• Motion in Two Dimensions

1) A car travelling with a speed of 60 km/h can 5) The velocity acquired by a body moving with
stop within a distance of 20 m. If the car is uniform acceleration is 30 ms−1 in 2 s and 60
going twice as fast, i.e., 120 km/h, the ms−1 in 4 s. The initial velocity is
stopping distance will be
A) zero B) 2 ms−1
A) 60 m B) 40 m C) 20 m D) 80 m
C) 3 ms−1 D) 10 ms−1
2) A body falls freely from the top of a tower.It
covers 36 % of the total height in the last 6) Two bikes A and B start from a point. A
second before striking the ground level. The moves with uniform speed 40 m/s and B
height of the tower is starts from rest with uniform acceleration 2
m/s2 . If B starts at t = 10 and A starts from
A) 50 m B) 75 m C) 100 m D) 125 m the same point at t = 10 s, then the time
during the journey in which A was ahead of B
3) A thief is running away on a straight road in is
jeep moving with a speed of 9 ms−1 A police
man chases him on a motor cycle moving at
A) 20 s
a speed of 10 ms−1 . If the instantaneous
separation of the jeep from the motorcycle is
B) 8 s
100 m, how long will it take for the police to
catch the thief
C) 10 s
A) 1 s B) 19 s C) 90s D) 100s
D) A is never ahead of B
4) A body is released from the top of a tower of
height H m. After 2 s, it is stopped and then 7) A particle is thrown upwards from ground. It
instantaneously released. What will be its experiences a constant air resistance force
height after next 2 s? which can produce a retardation of 2 m/s2 .
The ratio of time of ascent to the time of
A) (H− 5)m B) (H−10)m descent is
r r
2 2 3
A) 1:1 B) C) D)
C) (H−20)m D) (H−40)m 3 3 2
8) A stone is dropped from the top of a tower. 14) A body is projected upwards with a velocity
When it has fallen by 5 m from the top, u. It passes through a certain point above the
another stone is dropped from a point 25 m ground after t1 . The time after which the
below the top. If both stones reach the body passes through the same point during
ground at the same moment, then height of the return journey is
the tower is (take g = 10 m/s2 )    
u 2 u
A) −t1 B) 2 −t1
g g
A) 45 m B) 50 m C) 60 m D) 65 m  2   2 
u u
9) Two objects moving along the same straight C) 3 −t D) 3 −t1
g 1 g2
line are leaving point A with an acceleration
a, 2a and velocity 2u, u respectively at time 15) A person is throwing two balls in the air one
t=0. The distance moved by the object with after the other. He throws the second ball
respect to point A when one object overtakes when the first ball is at the highest point. If
the other is he is throwing the balls every second, how
high do they rise?
3u2 2u2 4u2 6u2
A) B) C) D)
a a a a A) 5 m B) 3.75 m C) 2.50 m D) 1.25 m
10) The relation between time t and distance x is
t = αx2 + βx where α and β are constants. 16) The other half of the distance is covered in
The retardation is two equal time intervals with speed of 4.5 m/s
and 7.5 m/s respectively. The average speed
of the particle during this motion is
A) 2αv3 B) 2βv3 C) 2 αβv3 D) 2β2 v3

11) A particle is moving in a straight line and A) 4.0 m/s B) 5.0 m/s
passes through a point O with a velocity of 6
ms−1 .The particle moves with a constant C) 5.5 m/s D) 4.8 m/s
retardation of 2 ms−1 for 4 s and there after
moves with constant velocity. How long after 17) A ball is released from the top of a tower of
leaving O does the particle return to O? height h. It takes time T to reach the ground.
What is the position of the ball (from ground)
A) 3 s B) 8 s C) never D) 4 s after time T/3?

12) The displacement x of a particle moving in A) h/9 m B) 7h/9 m

one dimension under the action of a constant
force
√ is related to time t by the equation C) 8h/9 m D) 17h/18 m
t = x + 3 , where x is in meters and t is in
seconds. Find the displacement of the 18) An insect moving along a straight line,
particle when its velocity is zero. travels in every second distance equal to the
magnitude of time elapsed. Assuming
A) Zero B) 12 m C) 6 m D) 18 m acceleration to be constant, and the insect
starts at t=0. Find the magnitude of initial
13) A thief is running away on a straight road in a velocity of insect
jeep moving with a speed of 9 ms−1 . A
policeman chases him on a motor cycle 3 5 1
A) unit B) unit C) 2 unit D) unit
moving at a speed of 10 ms−1 . If the 2 4 2
instantaneous separation of the jeep from the 19) A car starting from rest accelerates at the
motor cycle is 100 m, how long will it take for rate f through a distance S, then continues at
the policeman to catch the thief? constant speed for time t and then
decelerates at the rate f/2 to come to rest. If
A) 1 s B) 19 s C) 90 s D) 100 s the total traversed is 15S, then
 1 2 1 2 gD2
A) S = ft B) S = ft A) D sin θ − B)
4 2 2v20 sin2 θ gD2
1 D cos θ −
C) S = ft2 D) None of these 2v20 cos2 θ
6
gD2 gD2
20) A particle slides from rest from the topmost C) D tan θ − D) D tan θ −
point of a vertical circle of radius r along a 2v20 cos2 θ 2v20 sin2 θ
smooth chord making an angle θ with the 25) A train of 150 m length is going toward north
vertical. The time of descent is direction at a speed of 10 ms−1 . A parrot flies
at a speed of 5 ms−1 toward south direction
A) Least for θ = 0 parallel to the railway track. The time taken
by the parrot to cross the train is equal to
B) Maximum for θ = 0
A) 12 s B) 8 s C) 15 s D) 10 s
C) Least for θ = 45◦
26) The horizontal range and maximum height
D) Independent of θ attained by a projectile are R and H,
respectively. If a constant horizontal
21) The distances moved by a freely falling body acceleration a = g/4 is imparted to the
(starting from rest) during 1 st, 2nd, 3rd,..., projectile due to wind, then its horizontal
nth second of its motion are proportional to range and maximum height will be
 
H H
A) Even numbers A) (R + H), B) R + , 2H
2 2

B) Odd numbers C) (R + 2H), H D) (R + H), H

C) All integral numbers 27) A man who can swim at the rate of 2 km/hr
(in still river) crosses a river to a point
D) Squares of integral numbers exactly opposite on the other bank by
swimming in a direction of 120◦ to the flow of
22) A 2 − m wide truck is moving with a uniform the water in the river. The velocity of the
speed v0 =8 ms−1 along a straight horizontal water current in km/hr is
road. A pedestrian starts to cross the road
with a uniform speed v when the truck is 4 m A) 1 B) 2 C) 1/2 D) 3/2
away from him. The minimum value of v so
that he can cross the road safely is 28) A hose lying on the ground shoots a stream
of water upward at an angle of 60◦ to the
A) 2.62 ms−1 B) 4.6 ms−1 horizontal with the velocity of 16 ms−1 . The
height at which the water strikes the wall 8 m
C) 3.57 ms−1 D) 1.414 ms−1 away is

23) In a projectile motion, velocity at maximum A) 8.9 m B) 10.9 m C) 12.9 m D) 6.9 m

height is
29) Velocity of a particle at time t = 0 is 2 m/s. A
u cosθ constant acceleration of 2 m/s2 act on the
A) B) u cosθ
2 particle for 2 s at an angle 60◦ with the initial
u sinθ velocity. The magnitude of velocity of
C) D) None of these
2 particle at the end of 2 s will be
24) A cannon on a level plane is aimed at an √ √
angle θ above the horizontal and a shell is A) 2 5m/s B) 2 7m/s
fired with a muzzle velocity v0 towards a √ √
vertical cliff a distance D away. Then the C) 2 6m/s D) 2 3m/s
height from the bottom at which the shell
strikes the side walls of the cliff is
30) A ball is thrown from a point with a speed v0 35) A particle is projected from the ground with
at an angle of projection θ . From the same an initial speed of v at an angle θ with
point and at the same instant, a person starts horizontal. The average velocity of the
running with a constant speed v0 /2 to catch particle between its point of projection and
the ball. Will the person be able to catch the highest point of trajectory is
ball? If yes, what should be the angle of
vp vp
projection? A) 1 + 2cos2 θ B) 1−2cos2 θ
2 2
A) Yes, 60◦ B) Yes, 30◦ vp
C) 1 + 3cos2 θ D) v cosθ
2
C) No D) Yes, 45◦ 36) A swimmer crosses a flowing stream of width
w to and fro in time t1 . The time taken to
31) A ball rolls off the top of a staircase with a cover the same distance up and down the
horizontal velocity ums−1 . If the steps are h stream is t2 . If t3 is the time the swimmer
metre high and b metre wide, the ball will hit would take to swim a distance 2w in still
the edge of the nth step, if water, then
2hu 2hu2
A) n = B) n = A) t21 = t2 t3 B) t22 = t1 t3
gb2 gb
2hu2 hu2
C) n = D) n = C) t23 = t1 t2 D) t3 = t1 + t2
gb2 gb2
32) A number of bullets are fired in all possible 37) A projectile is given an initial velocity of î + 2ĵ
directions with the same initial velocity u. .The cartesian equation of its path is
The maximum area of ground covered by (g=10ms−2 ).
bullets is
 2 2  2 2 A) y=2x−5x2 B) y= x−5x2
u u
A) π B) π
g 2g C) 4y=2x−5x2 D) y=2x−25x2
 2  2
u u
C) π D) π 38) A water fountain on the ground sprinkles
g 2g
water all around it. If the speed of water
33) The trajectory of a projectile in a vertical coming out of the fountain is v, the total area
plane is y=ax−bx2 , where a and b are around the fountain that gets wet is
constants and x and y are, respectively,
v2 v4 π v4 v2
horizontal and vertical distances of the A) π B) π C) D) π
projectile from the point of projection. The g g2 2 g2 g2
maximum height attained by the particle and 39) Two stones are projected with the same
the angle of projection from the horizontal speed but making different angles with the
are horizontal. Their ranges are equal. If the
angle of projection of one is π /3 and its
b2 a2
A) , tan−1 (b) B) , tan−1 (2b) maximum height is h1 , then the maximum
2a b
height of the other will be
a2 2a2
C) , tan−1 (a) D) , tan−1 (a)
4b b A) 3 h1 B) 2 h1 C) h1 /2 D) h1 /3
34) A particle is moving along a circular path
with uniform speed. Through what angle 40) Referring to question−60, the ratio of the
does its angular velocity change when it range of the particle and its maximum range
completes half of the circular path in the inclined plane is
√ √
A) 0 B) 45 C) 180 D) 360 A) 1:2 B) 1: 2 C) 1: 3 D) 1:1
41) Two balls A and B are thrown with speeds u
and u/2, respectively. Both the balls cover the
same horizontal distance before returning to
the plane of projection. If the angle of
projection of ball B is 15◦ with the horizontal,
then the angle of projection of A is
   
1 1 1
A) sin−1 B) sin−1
8 2 8
   
1 1 1 1
C) sin−1 D) sin−1
3 8 4 8
42) For a given velocity, a projectile has the same
range R for two angles of projection if t1 and
t2 are the times of flight in the two cases then

A) t1 t2 ∝ R2 B) t1 t2 ∝ R
1 1
C) t1 t2 ∝ D) t1 t2 ∝
R R2
43) A particle is projected from a point O with a
velocity u in a direction making an angle α
upward with the horizontal. After some time
at point P, it is moving at right angle with its
initial direction of projection. The time of
flight from O to P is
u sin α u cos ecα
A) B)
g g
u tan α u sec α
C) D)
g g
44) A car is moving towards east with a speed of
25 kmh−1 . To the driver of the car, a bus
appears
√ to move towards north with a speed
of 25 3kmh−1 . What is the actual velocity of
the bus?

A) 50 kmh−1 , 30◦ E of N

B) 50 kmh−1 , 30◦ N of E

C) 25 kmh−1 , 30◦ E of N

D) 25 kmh−1 , 30◦ N of E

45) A ball thrown by one player reaches the other

in 2s. The maximum height attained by the
ball above the point of projection will be
about

A) 2.5 m B) 5 m C) 7.5 m D) 10 m