Question

A block of mass m moving with speed v compresses a spring through distance x before its speed is halved. The value of spring constant is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

We have

$K_i+U_i+W_{NC}=K_f+U_f$
$\frac{1}{2}m{v}^2+0+0=\frac{1}{2}m(\frac{v}{2}{)}^2+\frac{1}{2}k{x}^2$
$\Rightarrow \frac{3}{8}m{v}^2=\frac{1}{2}k{x}^2$
$\Rightarrow k=\frac{3m{v}^2}{4x^2}$