Question

A man of mass $50\text{kg}$ is standing on a platform of mass $200\text{kg}$ kept on a smooth horizontal surface. The man starts moving on the platform with a velocity $20\text{km/hr}$ relative to the platform. Find the recoil speed of the platform.

• A. $4\text{km/hr}$
• B. $2\text{km/hr}$
• C. $3\text{km/hr}$
• D. $1\text{km/hr}$

Answer 1

The correct option is A $4\text{km/hr}$


Mass of man, $m_m=50\text{kg}$
Mass of platform, $m_p=200\text{kg}$
Initially, both man and platform are stationary.
$\therefore v_{com}=0$
As there is no external force in horizontal direction, $a_{com}=0$
$\Rightarrow v_{com}$ will remain same (zero) even after man starts moving.

After man starts moving,
Given: velocity of man w.r.t platform is $v_{m/p}=20\text{km/hr}$.
Let recoil velocity of platform w.r.t ground be $v_p$ and velocity of man w.r.t ground be $v_m$.
$\Rightarrow v_m=v_{m/p}+(-v_p)=20\text{km/hr}-v_p$
$v_{com}=0$,
$\Rightarrow \frac{m_m{v}_m+m_p(-v_p)}{m_m+m_p}=0$
$\Rightarrow 50(20-v_p)-200v_p=0$
$\Rightarrow v_p=4\text{km/hr}$
$\therefore$ Recoil speed of platform$=4\text{km/hr}$