Question

Two boys $A$ and $B$ of mass $60\text{kg}$ and $40\text{kg}$ are standing on a platform. Both start walking towards each other with the same velocity $5\text{m/s}$. Find the velocity of the platform if mass of the platform is $100\text{kg}$.

• A. $0.5\text{m/s}$
• B. $2\text{m/s}$
• C. $1\text{m/s}$
• D. $5\text{m/s}$

Answer 1

The correct option is A $0.5\text{m/s}$


Given, mass of $A,m_1=60\text{kg}$
mass of $B,m_2=40\text{kg}$
and mass of platform, $m_3=100\text{kg}$

Let velocity of platform w.r.t ground be $v$ towards left, then velocity of boy $A$ w.r.t ground is $(5-v)$ towards right.
Similarly, velocity of boy $B$ w.r.t ground will is $(5+v)$ towards left.
i.e $v_1=5-v,v_2=-(5+v)$ and $v_3=-v$

Using momentum conservation, (treating rightwards direction as +ve)
$m_1{v}_1+m_2{v}_2+m_3{v}_3=0$
$60(5-v)-40(5+v)-100v=0$
$60\times 5-60v-40\times 5-40v-100v=0$
$300-200=200v$
$\Rightarrow v=\frac{100}{200}=0.5\text{m/s}$ (towards left)