Question

A toy gun uses a spring of force constant K. Before being triggered in the upward direction, the spring is compressed by a distance x. If the mass of the shot is m, on being triggered, it will go up to a maximum 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

$\frac{k{x}^2}{2mg}$

According to the law of conservation of energy, elastic potential energy stored in the spring = gravitational potential energy acquired by shot

$\frac{1}{2}k{x}^2=mgh$ or $h=\frac{k{x}^2}{2mg}$