Question

Two balls of same mass are released simultaneously from heights h & 2 h from the ground level. The balls collide with the floor & sticks to it. Then the velocity-time graph of centre of mass of the two balls is best represented by:

Answer 1

REF.Image.

Both balls A and B are released simultaneously, from

height h & 2h respectively .$(u_1=u_2=0)$

They compare motion in time $t_1=\sqrt{\frac{2h}{g}}$ and

$t_2=\sqrt{\frac{4h}{g}}$ respectively.

also from kinematics :- $v=u+at$ given,

$v_1=gt$ $v_2=gt$

also velocity of centre of man, $v_c=\frac{m_1{v}_1+m_2{v}_2}{m_1{m}_2}=\frac{m(v_1+v_2)}{2m}$

$=\frac{v_1+v_2}{2}$

for different time intervals, we get,

$v_c=gt,0<t<\sqrt{\frac{2h}{g}}$ both A & B move

$\frac{gt}{2},\sqrt{\frac{0}{g}}<t<\sqrt{\frac{4h}{g}}$, inly B moves

$0,t>\sqrt{\frac{4h}{g}},$ both come to wrt.

so, $v_c-t$ graph:-