A hollow sphere of mass 100g is released from the top of an inclined plane of inclination $ϕ = 45^{\circ}$ and height $h = 8 m$ . The coefficient of friction between the plane and the sphere is 0.25. The magnitude of work done (in J) by the force of friction as the sphere rolls down the inclined plane is ____

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Detailed Solution

$μ_{\min}$ for pure rolling $= \tan θ (\frac{β}{1 + β}) = 0 .4$

Here , for hollow sphere, $β = \frac{K^{2}}{R^{2}} = \frac{2}{3}$

Given $μ = 0 .25 < 0 .4$

Hence body rolls down with slipping

$W_{friction} = - f_{k} l = - (μmgcosθ) (\frac{h}{sinθ}) = - 2 J$

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