Question

Rohan drops a ball weighing 100 g from third floor (20 m) while Rahul drops a ball from the first floor (5 m).The momenta of both the balls are same when it hits the ground.
(i) Determine the momentum of the ball just before it hits the ground.

• A. $8.0kgm{s}^{-1}$
• B. $4.0kgm{s}^{-1}$
• C. $2.0kgm{s}^{-1}$
• D. $6.0kgm{s}^{-1}$

Answer 1

The correct option is C $2.0kgm{s}^{-1}$

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
$v=\sqrt{2\times a\times s}$
$v=\sqrt{2\times 10\times 20}$
$v=\sqrt{400}=20m/s$
$p=mv$
$p=0.1\times 20$
$p=20kgm{s}^{-1}$