Question

A 1kg block situated on a rough incline plane is connected to a spring of negligible mass having spring constant $100N{m}^{-1}$ as shown in the figure. The block is released from rest with the spring in the unstretched position. The block moves 10cm down the incline before coming to rest. The coefficient of friction between the block and the incline is (take g = $10m{s}^{-2}$ and assume that the pulley is frictionless)

• A. 0.2
• B. 0.3
• C. 0.5
• D. 0.6

Answer 1

The correct option is B

0.3

In equilibrium,

Work done = Potential energy of stretched spring

$mg(sin\theta -\mu cos\theta )x=\frac{1}{2}k{x}^2$

$2mg(sin\theta -\mu cos\theta )=kx$

$2\times 1\times 10\times (sin{45}^{\circ }-\mu cos{45}^{\circ })=100\times 10\times {10}^{-2}$

$sin{45}^{\circ }-\mu cos{45}^o=\frac{1}{2}$

$\frac{1}{\sqrt{2}}-\frac{\mu }{\sqrt{2}}=\frac{1}{2}$

$1-\mu =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}\Rightarrow \mu =1-\frac{1}{\sqrt{2}}=\frac{\sqrt{2}-1}{\sqrt{2}}$

$=\mu =0.3$