Question

Two objects of mass ratio $1:4$ are dropped from the same height. Then

• 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 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 $m_1$ and $m_2$, $u_1,u_2$ be their initial velocities respectively. Let $h$ be the height from where the objects are dropped. Let $v_1,v_2$ be the their final velocities and $t_1,t_2$ be the time taken to strike the ground respectively.
$u_1=u_2=0,h_1=h_2=h$
$h=\frac{1}{2}g{t}_1^2$ .........$\left(1\right)$
$h=\frac{1}{2}g{t}_2^2$ .........$\left(2\right)$
$\therefore t_1=t_2=t=\sqrt{\frac{2h}{g}}$ ..........$\left(3\right)$
now $v_1=g{t}_1{v}_2=g{t}_2$
From equation $\left(3\right),v_1=v_2=gt$
$\therefore \frac{v_1}{v_2}=\frac{1}{1}$