A 1 ~kg block situated on a rough incline is connected to a spring of negligible mass having spring constant 100 Nm ⁻¹ as shown in the figure. The block is released from rest with the spring in the unstretched position. The block moves 10 ~cm down the incline before coming to rest. The coefficient of friction between the block and the incline is (Take g =10 ~ms ⁻² and assume that the pulley is frictionless).

Step-by-step solution

The correct option is B 0.3 Here, m=1 ~kg , =45^ , k =100 ~N ~m ⁻¹ From figure, N=m g = N = mg where is the coefficient of friction between the block and the incline. Net force on the block down the incline, aligned & =m g -f & =m g - m g =m g( - ) aligned Distance moved, x=10 ~cm =10 10⁻² ~m In equilibrium, Work done = Potential energy of stretched spring aligned & m g( - ) x= 1 2 k x^2 & 2 m g( - )=k x & 2 1 10 ( 45^ - 45^ )=100 10 10⁻² aligned aligned & 45^ - 45^ = 1 2 & 1 2 - 2 = 1 2 & 1- = 2 2 = 1 2 =1- 1 2 =