Question

Two objects of mass ratio 1 : 4 are dropped from the same height. The ratio between their velocities when they strike the ground is:

• A. Both objects will have the same velocity.
• B. The velocity of the first object is twice that of the second one.
• C. The velocity of the $2^{nd}$ object is one fourth of that of the $1^{st}$ object.
• D. The velocity of the $2^{nd}$ object is 4 times of that of the $1^{st}$ one.

Answer 1

The correct option is A Both objects will have the same velocity.

Let the masses of the two objects be $m_1,m_2,$
Let $u_1,u_2,$ be their initial velocities respectively. Let h be the height from where the objects are dropped.
Let $v_1,v_2$ be the final velocities respectively.
Let $t_1,t_2$ be the time taken to strike the ground
$u_1=u_2=0,h_1=h_2=h$
$h=\frac{1}{2}g{t}_1^2......\left(a\right)$
$h=\frac{1}{2}g{t}_2^2......\left(b\right)$
$\therefore t_1-t_2=t=\sqrt{\frac{2h}{g}}.....\left(c\right)$
Now, $v_1=g{t}_1,v_2=g{t}_2$
From equation (c)
$v_1=v_2=gt$
$\therefore \frac{v_1}{v_2}=\frac{1}{1}$