Question 109: Centre of Mass and Rotational Motion

Question

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass?
(Assume the collision to be head-on elastic collision)

Accepted Answer

For a head on elastic collision
$${v_2} = {{m{u_1}} \over {m + 5m}} + {{m{u_1}} \over {m + 5m}}$$
$$ = {{2{u_1}} \over 6}$$ or $${{{u_1}} \over 3}$$
Initial kinetic energy of first mass $$ = {1 \over 2}mu_1^2$$
Final kinetic energy of second mass
$$ = {1 \over 2} 	imes 5m{\left( {{{{u_1}} \over 3}} ight)^2}$$
$$ = {5 \over 9}\left( {{1 \over 2}mu_1^2} ight)$$
$$\Rightarrow$$ kinetic energy transferred = 55% of initial kinetic energy of first colliding mass

Answer

50.0%

Answer

66.6%

Answer

55.6%

Answer

33.3%

Centre of Mass and Rotational Motion

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)

Choose the correct answer: