Question

A dart is loaded into a spring-loaded toy dart gun by compressing the spring by a distance of $d$. For the next loading, the spring is compressed by a distance $2d$. How much faster does the second dart leave the gun compared to first?

• A. Four times
• B. Two times
• C. Half times
• D. One-fourth times

Answer 1

The correct option is B Two times

The energy stored in the dart due to the compression of spring gets converted into kinetic energy. If $m$ is the mass of the dart, then $\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$

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

now x=2d (given)

$v_1=d\sqrt{\frac{k}{m}}⟹v_1$

$v_{2=}2d\sqrt{\frac{k}{m}}⟹2v_1$