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  4. A block of mass m=0.1 kg is released from a height of 4 m on a curved smooth surface. On the horizontal surface, path AB is smooth and path BC is rough with a coefficient of friction μ =0.1 . If the impact of the block with the vertical wall at C is perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be (take g=10 m s- 2 ) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-d6wvikycxnwo.png />

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Q. A block of mass $m=0.1 \, kg$ is released from a height of $4 \, m$ on a curved smooth surface. On the horizontal surface, path $AB$ is smooth and path $BC$ is rough with a coefficient of friction $\mu =0.1$ . If the impact of the block with the vertical wall at $C$ is perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be (take $g=10 \, m \, s^{- 2}$ )

Question

NTA AbhyasNTA Abhyas 2020Work, Energy and Power

Solution:

Total $KE$ dissipated against friction $=mgh=4J$
Work done against friction in one trip across $BC=mgμ\times 2=0.2J$
$\therefore $ Total number of trips across $BC=\frac{4}{\text{0.2}}=20$
$\therefore $ Total distance $=20\times BC+19\times AB=59m$