Question

A toy gun uses a spring of very large value of force constant $k$. When charged before triggered in the upward direction, the spring is compressed by a small distance $x$. If mass of shot is $m$, on being triggered it will go upto a height of:

• A. $\frac{k{x}^2}{mg}$
• B. $\frac{x^2}{kmg}$
• C. $\frac{k{x}^2}{2mg}$
• D. $\frac{k^2{x}^2}{mg}$

Answer 1

The correct option is C $\frac{k{x}^2}{2mg}$

$\begin{array}{c}springpotentialenergy,\\ u_1=\frac{1}{2}k{x}^2\\ wherexistheex\tan sionnaturallengthofthesprign.\\ Gravitationalpotentialenergy\\ u_2=mgh\\ Bylawofenergyconservation\\ u_1=u_2\\ \Rightarrow \frac{1}{2}k{x}^2=mgh\\ \Rightarrow h=\frac{k{x}^2}{2mg}\end{array}$

Hence,

option $\left(C\right)$ is correct answer.