Question

A spring gun of spring constant $90Nc{m}^{-1}$ 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. $60m{s}^{-1}$
• E. $90m{s}^{-1}$

Answer 1

The correct option is E

$90m{s}^{-1}$

Step 1: Given data

Spring constant $k=90Nc{m}^{-1}$

Compressed $x=12cm$

Mass of ball, $m=16g$

Step 2: Find the velocity of the ball

Let the velocity of the ball $=v$

Potential energy $=U$

Kinetic energy$=K.E$

The potential energy stored in the spring is,

$$\begin{gathered} U=(1/2)K{x}^2 \\ U=(1/2)\times 90\times {10}^2\times {(0.12)}^2 \\ U=64.8J \end{gathered}$$

The kinetic energy of the ball is,

$$\begin{gathered} K.E=(1/2)m{v}^2 \\ K.E=(1/2)\times 16\times {10}^{-3}\times v^2 \end{gathered}$$

According to the law of conservation of energy,

The potential energy stored in the spring = kinetic energy of the ball

$$\begin{gathered} 64.8=(1/2)\times 16\times {10}^{-3}\times v^2 \\ {v}^2=8100 \\ v=90m/s \end{gathered}$$

Hence, the velocity of the ball is $90m/s$.

Hence, option E is correct.