Question

A $15gm$ ball is shot from a spring whose spring has a force constant of $600N/m$. The spring is compressed by $5cm$. The greatest possible horizontal range of the ball for this compression is

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

Answer 1

The correct option is D $10.0m$

As we know,
$R_{max}=\frac{u^2}{g}$ at $\theta ={45}^{\circ }$
As per the information in question,
$(\frac{1}{2}m{u}^2=\frac{1}{2}k{x}^2)$
$R_{max}=\left(\frac{m{u}^2}{2}\right)\left(\frac{2}{mg}\right)=\left(\frac{1}{2}k{x}^2\right)\left(\frac{2}{mg}\right)$
$R_{max}=\frac{k{x}^2}{mg}\dots \left(i\right))$
Substituting the values in equation $\left(i\right)$
$R_{max}=\frac{\left(600\right)(5\times {10}^{-2}{)}^2}{(1.5\times {10}^{-3})\left(10\right)}$
$R_{max}=10.0m$

Final Answer: (c)