A solid cylinder of mass 3 ~kg is rolling on a horizontal surface with velocity 4 ~ms ⁻¹ . It collides with a horizontal spring of force constant 200 Nm ⁻¹ . The maximum compression produced in the spring will be

Step-by-step solution

Loss in KE = Gain in spring energy 1 2 m v^2 [1+ K^2 R^2 ]= 1 2 k x_ ^2 where k is the force constant. Given, v=4 ~m / s , m=3 ~kg , k=200 ~N / m For solid cylinder, K^2 R^2 = 1 2 1 2 3 (4)^2 [1+ 1 2 ]= 1 2 200 x_ ^2 The maximum compression in the spring x_ max =0.6 ~m