Question

A 15 gm ball is shot from a spring gun whose spring has a force constant of 600 N/m. The spring is compressed by 5 cm. The greatest possible horizontal range of the ball for this compression is $(g=10m/s^2)$

• A. 6.0 m
• B. 12.0 m
• C. 10.0 m
• D. 8.0 m

Answer 1

The correct option is C 10.0 m

$R_{max}=\frac{u^2}{g}=\left(\frac{1}{2}m{u}^2\right)\left(\frac{2}{mg}\right)=\left(\frac{1}{2}k{x}^2\right)\left(\frac{2}{mg}\right)=\frac{k{x}^2}{mg}(\because \frac{1}{2}m{u}^2=\frac{1}{2}k{x}^2)=\frac{600(0.05{)}^2}{0.015\times 10}=10m$
[Note : The actual value of 'u' will be less than the calculated value as some part of $\frac{1}{2}k{x}^2$ is used up in doing work against gravity when the spring regains its length]