Question

Rohan drops a ball weighing 100 g from third floor (20 m) while Rahul drops a ball from the first floor (5 m). If the momenta of both the balls are same when it hits the ground, determine the mass of the ball that Rahul dropped.​

• A. 100 g
• B. 200 g
• C. 400 g
• D. 300 g

Answer 1

The correct option is B 200 g

Given:
$m_1=100g=0.1kg$
$h_1=20m$
$h_2=5m$
$a=g=10m/s$ (As balls are in free fall)
$u=0m/s$ (As the balls are dropped from rest)
$p_1=p_2$ (Final momentum for each of the balls is the same)

Using the 3rd equation of motion, we get:
$v^2=u^2+2as$
$v_2=2as$ (Given u = 0)
Acceleration is constant
$v\propto \sqrt{s}$

Since momentum is the same:
$p_1=p_2$
$m_1{v}_1=m_2{v}_2$
$\frac{v_2}{v_1}=\frac{m_1}{m_2}$
$\frac{{\sqrt{s}}_2}{{\sqrt{s}}_1}=\frac{m_1}{m_2}...(\because v\propto \sqrt{s})$
$m_2=0.1\times \sqrt{\frac{20}{5}}=0.2kg$