Question

A spring of force constant $k=100N/m$ is compressed to $x=0.5m$ by a block of mass $100g$ released. Find the distance $d$ where it falls.

• A. $5m$
• B. $10m$
• C. $15m$
• D. $20m$

Answer 1

The correct option is B

$10m$

Step 1: Given data

Force constant, $k=100N/m$

Compressed $x=0.5m$

mass $m=100g$

Step 2: Find the velocity

The horizontal velocity with which the block will leave the surface,

$0+(½)k{x}^2=(½)m{v}^2+0$

Therefore,

$v=\sqrt{\frac{k}{m}}.x$

$v=5\sqrt{10}m/s$

Step 3: Find the distance

The horizontal distance moved by the block is given by

$d=vt$

$d=v\sqrt{\frac{2H}{g}}$

$$\begin{gathered} d=5\sqrt{10}\sqrt{\frac{2H}{g}} \\ d=5\sqrt{10}\sqrt{\frac{2\times 2}{10}} \\ d=10m \end{gathered}$$

Hence, Option B is correct.