Question

A stone of mass $500 \, g$ is dropped from the top of a tower of $100 \, m$ height. Simultaneously another stone of mass $1 \, kg$ is thrown horizontally with a speed of $10 \, m \, s^{- 1}$ from same point. The height of the centre of mass of the above two stone system after $3 \, sec$ is $\left(g = 10 \, m \, s^{- 2}\right)$

• A. $45 \, m$
• B. $35 \, m$
• C. $55 \, m$
• D. none of these

Answer 1

Answer: (C)

If height of stones is $h_{1}$ and $h_{2}$ after $t=3 \, sec$ then,
$h_{1}=100-\frac{1}{2}gt^{2}=55 \, m$
$h_{2}=100-\frac{1}{2}gt^{2}=55 \, m$
$\therefore $ height of centre of mass of the two stone system,
$h_{C M}=\frac{m_{1} h_{1} + m_{2} h_{2}}{m_{1} + m_{2}}=55 \, m$