In the arrangement shown in the figure mass of the block B and A are $$2$$ m,,$$8$$ m respectively. Surface between B and floor is smooth. The block B is connected to block C by means of a pulley. If the whole system is released then the minimum value of mass of the block C so that the block A remains stationary with respect to B is: (Coefficient$$ of friction between A and B is μ and pulley is $$ideal)

Question

In the arrangement shown in the figure mass of the block B and A are $$2$$ m,,$$8$$ m respectively. Surface between B and floor is smooth. The block B is connected to block C by means of a pulley. If the whole system is released then the minimum value of mass of the block C so that the block A remains stationary with respect to B is: (Coefficient$$ of friction between A and B is μ and pulley is $$ideal)

Infinity Learn · Accepted Answer

FBD of AIf the acceleration of ‘C’ is aFor block ‘A’ N $$=$$ $$8ma$$ $$-------(1)$$          $$8mg=$$μN $$=$$ μ$$8ma-------(2)$$    $$a=$$ gμand acceleration a can be written by the equation of system $$(A+B+C)m1g$$ $$=$$ $$(10$$ m $$+$$ $$m1)a----(3)8mg$$ $$=$$ μ$$8m(m1g10m$$ $$+$$ $$m1)10m$$ $$+m1$$ $$=$$ μ$$m110m$$ $$=$$ $$($$μ$$-1)m1$$⇒$$m1$$ $$=$$ $$10m$$μ$$-1$$

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