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A block B of mass \( 4 \mathrm{kg} \) is placed on a rough horizontal plane. A time dependent horizontal plane. A time dependent horizontal force \( \boldsymbol{f}=\boldsymbol{k} \boldsymbol{t}^{2} \) acts on the block, \( k=2 N / s^{2} . \) The frictional force between the block and the plane at \( \boldsymbol{t}=2 \sec \) is \( \boldsymbol{\mu}=\mathbf{0 . 2} \)

1. 4 N
2. 8N
3. 12 N
4. zero

Correct answer: 8N

Solution

At t = 2 s, the applied force is f = kt^2 = 2×(2^2) = 8 N. Since the block is on a rough horizontal plane, the frictional force at that instant matches the opposing force up to its limiting value, which here is consistent with 8 N.

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