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 n E   N   m - 1 for n = _____.

Step-by-step solution

Using work - energy theorem W net = ∆ K E W net   = K f - K i ⇒ - 1 2 K x 2 = 1 2 m v 2 2 - 1 2 m v 2 ⇒ - 1 2 K x 2 = E 4 - E ⇒ 1 2 K x 2 = 3 E 4 ⇒ K = 3 E 2 x 2 ⇒ K = 3 E 2 × 1 4 2 = 24 E   N   m - 1 Thus, the value of n = 24 .