Question

# A spring of spring constant $$k$$ placed horizontally on a rough horizontal surface. It is compressed against a block of mass m which is placed on rough surface, so as to store maximum energy in the spring. If the coefficient of friction between the block and the surface is $$\mu$$, the potential energy stored to the spring is : (block does not slide due to force of spring.)

A
μ2m2g24k
B
2μm2g2k
C
μ2m2g22k
D
3μ2mg2k

Solution

## The correct option is C $$\dfrac { { \mu }^{ 2 }{ m }^{ 2 }{ g }^{ 2 } }{ 2k }$$Equating force we get $$\mu mg=kx$$$$x=\dfrac{\mu mg }{k}$$Potential energy $$PE=\dfrac{1}{2}kx^2=\dfrac{1}{2}\dfrac{\mu^2m^2g^2}{k}$$Physics

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