A batsman deflects a ball by an angle of 45° without changing its initial speed which is
equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)
A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the
shell is 80 m s-1, what is the recoil speed of the gun ?
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.
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