Question

A body of mass $1\text{kg}$ falls freely from a height of $100\text{m}$, on a platform of mass $3\text{kg}$ which is mounted on a spring having spring constant $k=1.25\times {10}^6{\text{Nm}}^{-1}$. The body sticks to the platform, and the spring's maximum compression is found to be $x$. Given that $g=10{\text{ms}}^{-2}$, the value of $x$ will be close to:

• A. $4\text{cm}$
• B. $8\text{cm}$
• C. $80\text{cm}$
• D. $40\text{cm}$

Answer 1

The correct option is A $4\text{cm}$

By the principle of conservation of energy, the initial gravitational potential energy will be equal to the spring potential energy at maximum compression.

$\Rightarrow \frac{1}{2}k{x}^2=mgh$

$\Rightarrow x^2=\frac{2\times 1\times 10\times 100}{1.25\times {10}^6}$

$\Rightarrow x^2=16\times {10}^{-4}$

$\Rightarrow x=4\times {10}^{-2}\text{m}=4\text{cm}$

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