Question

A block of mass $m$ is attached to spring of force constant $k$ whose other end is fixed to a horizontal surface. Initially the spring is in its natural length and the block is released from rest. The average force acting on the surface by the spring till the instant when the block has zero acceleration for the first time is:

• A. $\frac{mg}{\pi }$
• B. $\frac{2mg}{\pi }$
• C. $\frac{3mg}{\pi }$
• D. $\frac{4mg}{\pi }$

Answer 1

Answer: (B)

$\frac{2mg}{\pi }$

Force will be O at $x=\frac{mg}{k}$

Time period of the oscillation will be $T=2\pi \sqrt{\frac{m}{k}}$.

By energy conservation,

$\frac{1}{2}k{x}^2+\frac{1}{2}m{v}^2=mg\left(x\right)$

This gives, $v=g\sqrt{\frac{m}{k}}$.

Thus average force will be $F_{avg.}=\frac{\Delta P}{t}=\frac{mv}{\frac{T}{4}}$

Hence, $F_{avg.}=\frac{2mg}{\pi }$.