Question

A boy of mass $50\text{kg}$ jumps to a height of $0.8\text{m}$ from the ground, then momentum transferred by the ground to the boy is -

• A. $400\text{kg-m/s}$
• B. $200\text{kg-m/s}$
• C. $800\text{kg-m/s}$
• D. $500\text{kg-m/s}$

Answer 1

The correct option is B $200\text{kg-m/s}$

Let the velocity of the boy when he left the ground is $v$.

From conservation of energy theorem,

$mgh=\frac{1}{2}m{v}^2$

$\Rightarrow v=\sqrt{2gh}=\sqrt{2\times 10\times 0.8}$

$\Rightarrow v=4\text{m/s}$

Therefore, momentum transferred by the ground is,

$p=mv=50\times 4=200\text{kg-m/s}$

​​​​​​​Hence, option $\left(B\right)$ is the correct answer.