Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s
-1
collide and rebound with the same speed. What is the impulse imparted to each ball due
to the other ?
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates
into two smaller nuclei the products must move in opposite directions.
Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible
string that goes over a frictionless pulley. Find the acceleration of the masses, and
the tension in the string when the masses are released.
Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal
surface are tied to the ends of a light string. A horizontal force F = 600 N is
applied to (i) A, (ii) B along the direction of string. What is the tension in the
string in each case?
Figure 4.16 shows the position-time graph of a particle of mass 4 kg. What is
the (a) force on the particle for t < 0, t > 4 s, 0 < t < 4 s? (b) impulse at t = 0 and
t = 4 s ? (Consider one-dimensional motion only).
A man of mass 70 kg stands on a weighing scale in a lift which is moving
(a) upwards with a uniform speed of 10 m s-1
,
(b) downwards with a uniform acceleration of 5 m s-2
,
(c) upwards with a uniform acceleration of 5 m s-2
.
What would be the readings on the scale in each case?
(d) What would be the reading if the lift mechanism failed and it hurtled
down freely under gravity ?
A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is
set into oscillation. The speed of the bob at its mean position is 1 m s-1
.
What is the trajectory of the bob if the string is cut when the bob is (a) at one
of its extreme positions, (b) at its mean position.
A truck starts from rest and accelerates uniformly at 2.0 m s-2. At t = 10 s, a
stone is dropped by a person standing on the top of the truck (6 m high from
the ground). What are the (a) velocity, and (b) acceleration of the stone at t =
11s ? (Neglect air resistance.)
A body of mass 0.40 kg moving initially with a constant speed of 10 m s-1 to
the north is subject to a constant force of 8.0 N directed towards the south
for 30 s. Take the instant the force is applied to be t = 0, the position of the
body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.
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