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Two block A and B each of mass $\frac{1}{2}$ kg is connected by a massless inextensible string and kept on horizontal surface. Coefficient of friction between block and surface shown in figure. A force F = kt (where k = 1 N/s and t is time in second) applied on A. Then (g = 10 m/s²)

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a

work done by friction force on block B is zero in time interval t = 0 to t = 3s.

b

work done by friction force on block A is zero in time interval t = 0 to t = 3s.

c

work done by tension on B is also zero in time interval t = 0 to t = 3s

d

speed of blocks at t = 10s is 27.5 m/s.

answer is A, B, C.

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Detailed Solution

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When t = 3s block just about to move and acceleration of block given by a $= \frac{t - 2}{1} t > 3$
$\begin{array}{l} \int_{0}^{v} dv = \int_{3}^{10} (t - 2) dt \\ v = \frac{t^{2}}{2} - {2 t|}_{3}^{10} = (50 - 20) - (\frac{9}{2} - 6) \\ = 30 + 1 .5 = 31 .5 m / s \end{array}$

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Two block A and B each of mass 12 kg is connected by a massless inextensible string and kept on horizontal surface. Coefficient of friction between block and surface shown in figure. A force F = kt (where k = 1 N/s and t is time in second) applied on A. Then (g = 10 m/s2)