Question

A block of mass ‘m’ (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when its speed is halved. The value of spring constant of used spring will be nE Nm–1 for n = _______.

Answer 1

When the velocity is halved the kinetic energy is reduced by a factor of $\frac{1}{4}$.
ΔKE= W all So $\frac{E}{4-E}$=−$\frac{1}{2}$K×(0.25)2×$\frac{3E}{4}$=$\frac{1}{2}$K×$\frac{1}{16}$K=24 E