Advertisements
Advertisements
Question
Two billiard balls A and B, each of mass 50 g and moving in opposite directions with speed of 5 ms–1 each, collide and rebound with the same speed. If the collision lasts for 10–3 s, which of the following statements are true?
- The impulse imparted to each ball is 0.25 kg ms–1 and the force on each ball is 250 N.
- The impulse imparted to each ball is 0.25 kg ms–1 and the force exerted on each ball is 25 × 10–5 N.
- The impulse imparted to each ball is 0.5 Ns.
- The impulse and the force on each ball are equal in magnitude and opposite in direction.
Advertisements
Solution
c and d
Explanation:
We are given that, m = 0.05 kg and v = 5 m/s
Hence we have initial momentum of each ball p = mv = 0.05 × 5 = 0.25 kg ms–1
After the collision, both balls will move in opposite directions
Hence, we have the final momentum of each ball p' = – mv = – 0.05 × 5 = – 0.25 kg ms–1
Now the impulse is the change in momentum,
Hence, I = p' – p = – 0.25 – 0.25 = – 0.5 kg ms–1.
APPEARS IN
RELATED QUESTIONS
An object of mass 1 kg travelling in a straight line with a velocity of 10 ms−1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
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.
Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s–2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)
A stream of water flowing horizontally with a speed of 15 m s–1 gushes out of a tube of cross-sectional area 10–2 m2, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?
Explain why, it is easier to stop a tennis ball than a cricket ball moving with the same speed.
What is the change in momentum of a car weighing 1500 kg when its speed increases from 36 km/h to 72 km/h uniformly ?
What is the momentum in kg.m/s of a 10 kg car travelling at (a) 5 m/s (b) 20 cm/s, and (c) 36 km/h ?
State the relation between the momentum of a body and the force acting on it.
A 10 g bullet travelling at 200 m/s strikes and remains embedded in a 2 kg target which is originally at rest but free to move. At what speed does the target move off ?
A gun of mass 3 kg fires a bullet of mass 30 g. The bullet takes 0.003 s to move through the barrel of the gun and acquires a velocity of 100 m/s. Calculate:
- the velocity with which the gin recoils.
- the force exerted on gunman due to recoil of the gun
Discuss the conservation of momentum in each of the following cases :
(i) a rocket taking off from ground.
(ii) flying of a jet aeroplane.
Why are car seat-belts designed to stretch some what in a collision ?
The troops (soldiers) equipped to be dropped by parachutes from an aircraft are called paratroopers. Why do paratroopers roll on landing ?
Why would an aircraft be unable to fly on the moon ?
A ball X of mass 1 kg travelling at 2 m/s has a head-on collision with an identical ball Y at rest. X stops and Y moves off. Calculate the velocity of Y after the collision.
A man wearing a bullet-proof vest stands still on roller skates. The total mass is 80 kg. A bullet of mass 20 grams is fired at 400 m/s. It is stopped by the vest and falls to the ground. What is then the velocity of the man?
Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of the initial and final momentums of the ball are the same. Yet, it is not an example of conservation of momentum. Explain why?
A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 ms–2)
