A mass of 1 kg falls from a height of 1 m and lands on a mass less platform supported by a spring having spring constant 15 N m - 1 as shown in the figure. The maximum compression of the spring is. (acceleration due to gravity = 10 m s - 2 )

Step-by-step solution

In case of maximum compression, total mechanical energy will be conserved. T E 1 = T E 2 Assuming dotted line to be reference for gravitational potential energy. ⇒ m g h + 0 = m g - x + 1 2 k x 2 ⇒ 1 × 10 × 1 = 1 × 10 × - x + 1 2 × 15 × x 2 ⇒ 3 x 2 - 4 x - 4 = 0 ⇒ x = 2   m