## Kumar Ketan is teaching live on Unacademy Plus

PROBLEMS OF COLLISIONS Advanced Level (Asked in IIT JEE)

A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length "L" (L>>r) and are at rest at random position. The rod is mounted between two rigid supports (see figures). If one of the beads is now given a speed "v', the average force experienced by each support after a long time is (assume all collisions are elastic) JEE (Main)Online-2015 2 (L- nr) (L- nr) (c) zero (d) mv2 (L- 2nr)

Fig-a

. Solution: Change in momentum in each collision with rigid support Space between the supports for motion of beads is "L-2nr" Time gap between two successive collision with same support = 2L_4nr 0 2mv

A particle of mass "m" moving in the X- direction with speed "2v" is hit by another particle of mass "2m" moving in the Y- direction with speed "v". If the collisions perfectly inelastic, the percentage loss in the energy during the collision is close to: 1 JEE Main (2015) (a) 56% (b) 62% (c) 44% (d) 50%

Solution: Before collision: 2v Y-axis 2m X-axis Kinetic energy Before collisionm (2v)2+ 2m (v)23mu2

After collision Applying Momentum conservation for inelastic collision 2mv 2 3 101- 22 0) 3

1 2 2 /2 3 2 4 3 5 3 Ki-K, 3 3mm) 5 5 ~ 56%

This question has statement 1 and statement 2. Of the four choices given after the Statements, choose the one that best describes the two statements Statement-1: A point particle of mass m moving with speed v collides with stationary point particle of mass M .If the maximum energy loss possible is given as f the Statment-2:Maximum energy loss occurs when the particles get stuck together as a result of the collision. n fm M+ m Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation of Statement-1 Statement-1 is true, Statement-2 is true, Statement-2 is a not correct explanation of Statement-1 Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true. 1. 2. 3. 4.