Question

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

• A. $50m{s}^{-1}$
• B. $90m{s}^{-1}$
• C. $40m{s}^{-1}$
• D. $60m{s}^{-1}$

Answer 1

The correct option is B $90m{s}^{-1}$

Potential energy stored in spring =kinetic energy of ball

Potential energy stored in spring ,$U=\frac{1}{2}K{x}^2$

given ,spring constant,$k=90N/cm=9000N/m$

compression ,$x=12cm=0.12m$

So,

$\begin{array}{c}U=\frac{1}{2}\times 9000\times {\left(0.12\right)}^2\\ =\frac{1}{2}\times 0.9\times 144\end{array}$

Let velocity of ball is $vm/s$

So, kinetic energy of ball, $K.E=\frac{1}{2}m{v}^2$

$=\frac{1}{2}\times 16\times {10}^{-3}\times v^2$

now,

$\begin{array}{c}\frac{1}{2}\times 0.9\times 144==\frac{1}{2}\times 16\times {10}^{-3}\times v^2\\ 0.9\times 144\times \frac{{10}^2}{16}=v^2\\ v^2=900\times \frac{144}{6}\\ v=90m/s\end{array}$