The coefficient of friction between the block and plank is μ and ground is smooth. The value of µ is

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The coefficient of friction between the block and plank is μ and ground is smooth. The value of µ is such that block becomes stationary with respect to plank before it reaches the other end. Then which of the following statement is incorrect.

Accepted Answer

Sol.mv0 = (M + m)v ⇒ v = $\frac{mv_{0}}{(M + m)}$$(\Delta K)_{system} = \frac{1}{9}(M + m)u^{2} - \frac{1}{2}mu_{0}^{3} = \frac{1}{9}(M + m)\left\lbrack \frac{mv_{0}}{M + m} \right\rbrack^{2} - \frac{1}{2}mv_{0}^{2}$$= \frac{1}{2}\left( \frac{m^{2}}{M + m} \right)u_{0}^{2} - \frac{1}{2}mv_{0}^{2} = \frac{1}{9}mv_{0}^{2}\left\lbrack \frac{m}{M + m} - 1 \right\rbrack$∴ Total work of friction is

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