Question

A spring gun of spring constant $90N/cm$ is compressed $12cm$ by a ball of mass $16g$ . If the trigger is pulled, the velocity of the ball is

• A. $50m{s}^{-1}$
• B. $9m{s}^{-1}$
• C. $40m{s}^{-1}$
• D. $\text{26 }m{s}^{-1}$
• E. $90m{s}^{-1}$

Answer 1

Answer: (E)

Kinetic energy of ball = potential energy of spring ie,
$\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$
$\therefore$ $16\times {10}^{-3}\times v^2=\frac{90}{{10}^{-2}}\times {(12\times {10}^{-2})}^2$
Or $v^2=\frac{90\times 144\times {10}^{-4}}{{10}^{-2}\times 16\times {10}^{-3}}$
Or $v=90m{s}^{-1}$