Question

A block of mass $2kg$ is on a smooth horizontal surface. A light spring of force constant $800N/m$ has one end rigidly attached to a vertical wall and lying on that horizontal surface. Now the block is moved towards the wall compressing the spring over a distance of $5cm$ and then suddenly released. By the time the spring regains its natural length and breaks contact with the block, the velocity acquired by the block will be :

• A. 200 m/s
• B. 100 m/s
• C. 2 m/s
• D. 1 m/s

Answer 1

Answer: (D)

1 m/s

Compression of the spring $x=5cm=5\times {10}^{-2}m$

Using conservation of energy:
Initial $M.E=$ Final $M.E$
i.e Potential energy spring $=$Kinetic energy of block
$\Rightarrow \frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$

Or $k{x}^2=m{v}^2$

$\Rightarrow 800\times 25\times {10}^{-4}=2\times v^2$
$\Rightarrow v=1m/s$