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Question (1 mark)
Q1. Is it possible
that a body can be treated simultaneously at rest as will as in motion?
Ans. Rest and motion are relative terms. A person sitting
in a moving bus is at rest with reference to the frame of the bus but in motion
with reference to the outside buildings, trees or poles.
Q2. A car moves at uniform speed of 60 km h^{1}
on straight road blocked by a wall. The jeep has to take a sharp perpendicular
turn along the wall. A fly rocket at uniform speed of 100 km h^{ –}
starts from the wall towards the jeep when jeep is 30 km away. The fly rocket
reaches the windscreen and returns to wall. What is the told distance covered
by fly rocket?
Ans. Time taken by car
to cover a distance of 30 km=
_{}
Total distance
covered by fly rocket in this duration = 100 ´ ˝ = 50 km
Q3. What is
represented by the area under a velocity time graph?
Ans. The velocities at different instants can he plotted
as shown in the figure. The graph here shows uniform velocity.
_{}
or distance, s
= v x t.
Thus area under a
velocity time graph gives displacement.
Q4. Pick the one
dimensional motion
(i) A bird flying
here and there is sky
(ii) Motion of a communication satellite around earth.
(iii) Rebounding of striker of a carom board.
(iv) Truck running on straight road.
Ans. Truck running on
a straight road is an example of one dimensional motion because in this case
motion is kept along a straight line.
Q5. It is correct to
say that a speedometer measures average speed?
Ans. No, a speedometer indicates instantaneous speed
only.
Q6. Give ratio of
speed to velocity of a moving object.
Ans. Velocity can be
less than or equal to speed
_{}
Q7. Can an object
have?
(i) Constant speed
bur variable velocity
(ii) Constant velocity but varying speed.
Ann. (i) Yes, eg. Uniform circular motion
(ii). No, because constant velocity means that both
magnitude and direction of velocity are fixed. Magnitude of velocity can be
taken as speed so in this case speed is also fixed.
Q8. Can time be taken
as negative?
Ans. Yes, positive and
negative are simply relative terms. If we take the instantaneous time before
the origin i.e. zero consideration of time then it can be taken as negative.
Q9. Can a body have zero velocity and finite
acceleration or can a particle in one dimension motion with zero speed at any instant
may have not zero acceleration at that instant.
Ans. Yes, a body can have non zero acceleration at any instant when speed is zero. If a ball is thrown vertically up it has zero velocity at the top moxt point and non zero acceleration due to gravity, g = 9.8 ms^{2}
Q10. If a body has
constant speed, is he true that it can have acceleration?
Ans. Yes, an object moving along a circular path with
constant speed has acceleration due to continuous change in direction.
Q11. A particle is one dimensional motion with positive
value of acceleration must be speeding up’. Do you agree with this statement?
Ans. It is a false
statement because in the case of initial velocity of a particle being negative,
the particle speeds down even if the acceleration is positive.
Q12. Is the
acceleration of an automobile greater when brakes are applied hard or when the
accelerator is given?
Ans. In the first case
the acceleration is greater because the car is suddenly stopped so the rate of
change of velocity i.e. acceleration is large.
Q13. One light and another heavy mass are thrown
vertically upwards with some initial speed. Which one will attain higher
height?
Ans. The height attained is independent of the mass of
body so with same initial speeds both will attain same height.
Q14. If a body has no
acceleration when if is moving with uniform velocity in a straight line, will
it be in equilibrium?
Ans. Yes, it is in
equilibrium because for equilibrium the next force should be zero i.e., net
acceleration should be zero.
Q15. Why does a
parachute descend slowly?
Ans. Due to retardation.
Question (2 marks)
Q1. What do you
understand by static’s, dynamics and kinematics?
Ans. Static’s is a branch of mechanics which deals
with the study of rest conditions of a body.
Dynamics is a branch of
mechanics which deals with the study of motion of objects taking into account
the cause of motion.
Kinematics is a branch of
mechanics which deals with the study of motion of objects without taking into
account the cause of motion.
Q2. In which of these
cases a body can be considered as point object:
(a)
a train moving
without jerks between two stations.
Ans. Since the motion
of the train between two distant stations is smooth throughout so keeping in
view the long distance covered between the two stations in reasonable duration
of time, the size of the train is neglected and it is considered as a point
object.
(b) A monkey sitting on top of a man cycling smoothly
on a circular track.
Ans. The distance covered by the monkey in reasonable
duration of time is more so tit is considered as a point object.
(c) A spinning cricket ball turns sharply on hitting
the ground.
Ans. Since the turning of the ball is not smooth but sharp so the distance
covered by it in reasonable duration of time is not large so this ball can not
be treated as a point object.
(d) A tumbling beaker
slipped off the edge of a table.
Ans. Since the beaker
is tumbling and then slipls off so the distance
covered by it in reasonable duration of time is not large so it is not treated
as a point object.
(e) Earth revolving around sun.
Ans. Size of earth is
too small as compared to radius of orbit around sun so it can be treated as a
point object.
Q3. The position time (xt) graphs for two children A
and B returning from their school O to their homes P and Q respectively are
shown. Choose the correct entries:
(a) (A/B) lives closer to the school than (B/A)
Ans. A lives closer to the school than B because B has
to cover higher distance [OP< OQ]
(b) (A/B) starts from the school earlier
than (B/A)
Ans. A starts from the school earliest than B because t^{
}= 0 for A but B has some finite time.
(c) (A/B) walks faster the (B/A)
Ans. B walks faster than A because it covers more
distance in less duration of time [slope of B is greater than that of A)
(d) A and B reach home at the (same/ different) time
Ans. A and B reach home at the same time.
(e) (A/B) overtakes (B/A) on the road (one/ twice)
Ans. B overtakes A on
the road once (at X i.e. the point of intersection.)
Q4. State with reasons which of these cannot possibly
represent one dimensional motion of a particle.
Ans. Figure (a) does not represent one dimensional
motion of particle because the particle has two different positions at the same
instant which is not the case of one dimensional motion. Figure (b) also does
not represent one dimensional motion of the particle because here the total
path length is shown to decrease with time which is not possible in one
dimensional motion.
Q5. What is
instantaneous velocity?
Ans. The velocity of a body at a particular position or instant
is called instantaneous velocity.
It is defined as
the limit of the average velocity of a body when time interval D t becomes
infinitesimally small i.e.
_{}
_{ }
Thus
instantaneous velocity is the rate of change of position of a moving body with
respect to time at that instant.
Q6. A man standing on the edge of a cliff throws a
store straight down with same initial speed u and then throws another stone
straight up with initial speed u and from the same position. Find ratios of speeds,
two stones would attain, when they hit ground at the base of the cliff.
Ans. The stone thrown upward reaches back to the thrown
with speed u.
Thus both the
stones fall under the influence of gravity with same initial velocity u so the
two stones will hit the ground with same speed. Hence ratio of their speeds
when they hit ground is 1.
Q7. Is variation of
time possible with position as shown?
Ans. No, because from
B to C position changes from x_{1} to x_{2} on positive direction
but time is shown to be reduced (t_{1} to zero) which is not possible.
Q8. Can an object have
(i) constant speed but variable velocity
Ans. (i) Yes, e.g uniform circular motion.
(ii) constant velocity but
varying speed.
Ans. No, because constant
velocity means that both magnitude and direction of velocity are fixed.
Magnitude of velocity can be taken as speed so in this case speed is also
fixed.
Q9. Give conditions
when
(i) magnitude of displacement
= distance
Ans. In case an object is having uniform motion in a
straight line.
(ii) magnitude of average
velocity = speed
Ans. In case an object is having uniform motion along a
straight line.
(iii) average velocity =
instantaneous velocity.
Ans. In case an object is having uniform motion in one
dimension.
Q10. Displacement of a body is given by a sin (vt + f) where a is amplitude, v is angular
velocity, t is time and f is phase difference. Find time for
maximum displacement.
Ans. For maximum displacement sin (wt + f) should be unity
i.e. (wt + f) = p/2 i.e.
wt = p/2  f
_{}
Question (3 marks)
Q1. Suggest a
physical situation for the following graphs?
Ans. Graph (a) may represent a particle
lying at rest on a smooth floor gets a kick to strike a wall. It then rebounds
to strike the opposite wall which ultimately stops it because the graph
indicates increased in distance with time then decrease in distance with time
leading to reversal of direction and then constant distance throughout.
Graph (b) may represent the
repeated bouncing of a particle which hits the floor and rebounds in hit the
floor again because the graph indicates repeated continuous drop in velocity
with time followed with reversal in the directions.
Graphs (c) may represent a
particle moving with uniform velocity hit for a very short duration in the
opposite direction because the graph shows the acceleration for a very short
time interval.
Q2. A driver driving a truck at constant speed of 20 ms^{1}
suddenly saw a parked car ahead of him by 95m. He could apply the brake after
some time to produce retardation of 2.5 ms^{2}. What is his reaction
time when accident is just avoided?
Ans. Let the driver apply the brakes at y then
S_{1}= 20
´ t
Using 2as= v^{2}u^{2},
we get,
2 (2.5) s_{2}
= 0  20^{2} ( because of retardation)
But 95 = s_{1}
+ s_{2}
Or s_{1}
= 95 – s_{2}= 95 – 80 = 15m
From (i), t = s_{1}/_{20 }= ^{15}/_{20}
= 0.75s.
Q3 A small ball rolls down a staircase with
uniform horizontal velocity u. If each step is y m high and x m wide, the
marble just hits the edge of the nth step. Find the value of n.
Ans. Total horizontal
distance to be covered
=
x ^{x}^{ }n = nx
Total
vertical distance to be covered
=
y ^{x} n = n
but nx = ut
(using s = ut + ˝ at^{2}) (1)
_{}
and
Substituting
the value of t from equation (i) in equation (ii)
_{}
Q4. A police van moving on a highway with a speed of 30
kmh^{1} fires a bullet a thief’s car speeding away in the same
direction with a speed of 192 km h1. If the muzzle speed of the bullet is 150
ms1, with what speed does the bullet hits the thief’s car?
Ans. Here velocity of police van (u_{v}),
muzzie velocity of bullet (v_{b}) and
velocity of car (v_{c}) are all in the same
direction.
_{}
v_{b}=
150 ms^{1} and v_{c} = 192 km/h^{1}
Effective velocity of bullet
_{}
Relative velocity of bullet w.r.t. car,
_{}
= 105 ms^{1}
Q1. A particle is projected with a velocity v,
so that its range on a horizontal plane is twice the greatest height attained.
If g is acceleration due to gravity, then its range is:
(a) 4v^{2}/5g (b) 4g/5v^{2} (c)
4v^{3}/5g^{2} (d)
4v/5g^{2}
Ans. (a)
Q2. During a projectile motion if the maximum
height equals the horizontal range, then the angel of projection with the
horizontal is
(a) tan^{1}
(1) (b) tan^{1} (2) (c) tan^{1}(3) (d) tan ^{–1} (4)
Ans. (d)
Q3. The point from where a ball is projected is
taken as the origin of the coordinate axes. The x and y components of its
displacement are given by x = 6t and y = 8t – 5t^{2}. What is the
velocity of projection?
(a) 6 ms^{1} (b) 8 ms^{1} (c)
10 ms^{1} (d) 14 ms^{1}
Ans. (c)
Q4. A particle is fired with velocity u making
angle q with the horizontal. What is the change in
velocity it is at the highest point?
(a) u cosq (b) u (c)
u sinq (d) (u cosq  u)
Ans. (c)
Q5. In the Q.4. the change is
speed is
(a) u cosq (b) u (c)
u sinq (d) (u cosq  u)
Ans. (d)
Q6. A ball whose kinetic energy is E, is thrown
at an angle of 45^{0} with the horizontal, its kinetic energy at the
highest point of its flight will be.
(a) E
_{}
_{}
(d) zero
Ans. (c)
Q7. Two bullets are
fired horizontally with different velocities from the same height. Which will
reach the ground firs?
(a) Slower
one
(b)
Faster one
(c)
Both will reach simultaneously
(d)
It cannot be predicted
Ans. (c)
Q8. A ball is thrown upwards and it returns to ground
describing a parabolic path. Which of the following quantities remains constant
throughout the motion?
(a) Kinetic energy of
the ball
(b) Speed of the ball
(c) Horizontal
component of velocity
(d) Vertical
component of velocity
Ans. (c)
Q9. An aero plane moving horizontally with a speed of
180 km/hr drops a food packet while flying as a height of 490 m. The horizontal
range is:
(a) 180 m (b) 980 m (c) 500 m (d)
670 m
Ans. (c)
Q10. The range of a
rifle bullet on level ground is 6000 m. The range at an incline of 30^{0}
is
(a) 4000 m (b) 2000 m (c) 6000 m (d)
1000 m
Ans. (a)
Q11. 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% (c) 40%
Ans. (a)
Q12. If the time of
flight of a projectile is doubled, what happens to the maximum height attained?
(a) Halved (b) Remains unchanged (c) Doubled (d) Becomes four times
Ans. (d)
Q13. A body of mass 2 kg has an initial velocity of 3
m/s along xaxis and it is subjected to a force of 4N in ydirection. The
distance of the body from origin after 4 seconds will be: (the body was
subjected to force at the origin at t=0)
(a) 12 m (b) 28 m (c) 20 m (d)
48 m
Ans. (c)
Q14. A body has an initial velocity of 3 m/s and has an
acceleration of 1 m/sec.2 normal to the direction of the initial velocity. Then
its velocity 4 seconds after the start is:
(a) 7 m/sec along the
direction of initial velocity
(b) 7 m/sec along the
normal to the direction of initial velocity
(c) 7 m/sec mid – way
between the two directions
(d) 5 m/sec at an
angle of tan^{1} (4/3) with the direction of initial velocity.
Ans. (d)
Q15. A person can
throw a stone to a maximum height of h metre. The maximum distance to which he
can throw the stone is:
(a) h (b) ^{h}/_{2} (c) 2h (d)
3h
Ans. (c)
Q16. An arrow is shot into the air Its
range is 2000 metres and its time of flight is 5 sec. If the value of g is
assumed to be 10 m/sec^{2}, then horizontal component of the velocity
of arrow is:
(a) 25 m/s (b) 40 m/s (c) 31.25 m/s (d)
12.5 m/s
Ans. (b)
Q17. In the Q. 16, the
maximum height attained by the arrow is:
(a) 12.5 m (b) 25 m (c) 31.25 m (d)
40 m
Ans. (c)
Q18. In the Q. 16, the
vertical component of the velocity is:
(a) 12.5 m/s
(b) 31.25 m/s
(c) 25 m/s
(d) 40 m/s
Ans. (c)
Q19. In the Q. 16, the
angle of projection with the horizontal is
_{}
_{}
_{}
_{}
Ans. (c)
Q20. The ceiling of a hall is 40 m high. For maximum
horizontal distance, the angle at which the ball may be thrown with a speed of
56 ms^{1} without hitting the ceiling of the hall is:
(a)
25^{0}
(b)
30^{0}
(c)
45^{0}
(d)
60^{0}
Ans. (b)
Q21. From the top of a tower 19.6 m high, a ball is
thrown horizontally. If the line joining the point of projection to the point
where it hits the ground makes and angle of 45^{0} with the horizontal,
then the initial velocity of the ball is:
(a)
9.8 ms^{1}
(b)
4.9 ms^{1}
(c)
14.7 ms^{1}
(d)
2.8 ms^{1}
Ans. (a)
Q22. Two tall buildings are 30 m apart. The speed with which a ball must be thrown horizontally from a
window. 150 m above the ground in one building so that it enters a
window 27.5 m from the ground in the other building is:
(a)
2 ms ^{1}
(b)
6 ms^{1}
(c)
4 ms^{1}
(d)
8 ms^{1}
Ans. (b)
Q23. A projectile will
cover the maximum vertical distance in the minimum time when the angle of
projection with vertical is
(a)
0^{0}
(b)
30^{0}
(c)
60^{0}
(d)
90^{0}
Ans. ( a)
Q24. Two paper screens A and B are separated by 150 m. A
bullet pierces A and then B. The hole in B is 15 cm below the hole in A. If the
bullet is traveling horizontally at the time of hitting A,
then the velocity of the bullet at A is.
_{}
_{}
_{}
_{}
Ans. (d)
Q25. The range of a projectile when fixed at 75^{0}
with the horizontal is 0.5 km. What will be its range when it is fired at an
angle of 45^{0}?
(a)
0.5 km
(b)
1.0 km
(c)
1.5 km
(d)
2.0 km
Ans. (b)
Q26. The time of flight
of a projection on an upward inclined plane depends upon:
(a)
angle of projection
(b) angle of inclination
of the plane.
(c) Air resistance
(d) (a) and (b) both
Ans. (d)
Q27. Which of the following
is larges, when the height attained by the projectile is the largest?
(a)
Range
(b)
Time of flight
(c)
Angle of projectile with vertical
(d)
None of above
Ans. (b)
Q28. A body of mass m is projected horizontally with a velocity
v from the top of a tower of height h and it reaches the ground at a distance x
from the foot of the tower. If a second body of mass 2m is projected
horizontally from the top of a tower of height 2h, it reaches the ground at a
distance 2x from the foot of the tower. The horizontal
velocity of the second body is:
(a) v
(b) 2v
_{}
_{}
Ans. (c)

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