Question

A block of mass 'm' moving at a speed V compresses a spring through a distance x before its speed is halved. The spring constant of the spring is

• A. $\frac{7m{V}^2}{4x^2}$
• B. $\frac{3m{V}^2}{4x^2}$
• C. $\frac{7m{V}^2}{8x^2}$
• D. None of these

Answer 1

The correct option is B $\frac{3m{V}^2}{4x^2}$


Let 'K' be the spring constant

By conservation of mechanical energy

$\frac{1}{2}m{V}^2=\frac{1}{2}m\times {\left(\frac{V}{2}\right)}^2+\frac{1}{2}K{x}^2$

Solving we get

$K=\frac{3m{V}^2}{4x^2}$