Question

A body of mass $1$kg falls freely from a height of $100$ m on a platform of mass $3$ kg which is mounted on a spring having spring constant $k=1.25106N/m$. The body sticks to the platform and the spring's maximum compression is found to be x. Given that $g=10m/s^2$, the value of $x$ will be close to :

• A. $4cm$
• B. $8cm$
• C. $80cm$
• D. None of these

Answer 1

Answer: (A)

$4cm$

Initial compression is negligible

Compression will be significant due to collision.

velocity after collision

$1\times \sqrt{2\times 10\times 100}=4+v$

$v=5\sqrt{5}$ m/s

Assuming this as maximum velocity

$v=\omega$ A

$5\sqrt{5}=\sqrt{\frac{1.25\times {10}^6}{4}}$ A

$A=5\times 2\times 2\times {10}^{-3}m=2$ cm