JEE MAIN - Physics (2022 - 27th June Morning Shift - No. 8)
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)
50.0%
66.6%
55.6%
33.3%
Explanation
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
$$ = {1 \over 2} \times 5m{\left( {{{{u_1}} \over 3}} \right)^2}$$
$$ = {5 \over 9}\left( {{1 \over 2}mu_1^2} \right)$$
$$\Rightarrow$$ kinetic energy transferred = 55% of initial kinetic energy of first colliding mass
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