CBSE Class 12 Physics Centre of Mass Basic Level Assignment

CBSE Class 12 Physics Centre of Mass Basic Level Assignment. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

1. A block of mass 10 kg is suspended from a 3 metre long weightless string. A bullet of mass 0.2 kg is fired into the block horizontally with a speed of 20 m/s and it gets embedded in the block. Calculate

(a) the speed acquired by the block
(b) the maximum displacement of the block
(c) the energy converted to heat in the collision.

2. A projectile of mass 50 kg is shot vertically upwards with an initial velocity of 100 m/sec. After 5 seconds it explodes into two fragments, one of which having mass 20 kg travels vertically up with a velocity of 150 metres/sec. If g = 9.8 m/s².
(a) What is the velocity of the other fragment at that instant ?
(b) Calculate the sum of the momenta of the two fragments 3 second after the explosion. What would have been the momentum of the projectile at this instant if there had been no explosion ?

3. Particles P and Q of masses 20 g and 40 g respectively are simultaneously projected from points A and B on the ground. The initial velocities of P and Q make angles 45º and 135º respectively with line AB. Each particle has an initial speed of 49 m/s. The separation AB is 245 m. Both particles travel in the same vertical plane and undergo a collision. After the collision, P retraces its path. Taking g = 9.8 m/s2, determine

(a) the position of Q when it hits the ground.
(b) How much time, after the collision, does Q take to reach the ground.

4. A shell of mass 500 kg travelling horizontally at a speed of 100 m/s explodes into just three parts. The first part of mass 200 kg travels vertically upwards at a speed of 150 m/s and the second part of mass 150 kg travels horizontally with a speed of 60 m/s, but in a direction opposite to that of the original shell. What is the velocity of the third part? What is the path of the centre of mass of the fragments after the explosion ?

5. A small sphere of mass 10 g is attached to a point of a smooth vertical wall by a light string of length 1 m. The sphere is pulled out in vertical plane perpendicular to the wall so that the string makes an angle of 60º with the wall and is then released. It is found that after the first rebound, the string makes a maximum angle of 30º with the wall. Calculate the coefficient of restitution and the loss of kinetic energy due to impact. If all the energy is converted into heat, find the heat produced by the impact.

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