Two blocks of masses $$M1$$ and $$M2$$, are connected with a string passing over a pulley as shown in figure. The block $$M1$$ lies on a horizontal surface. The coefficient of friction between the block $$M1$$ and the horizontal surface is μ. The system accelerates. What additional mass m should be placed on the block $$M1$$ so that the system does not accelerate?

Question

Two blocks of masses $$M1$$ and $$M2$$, are connected with a string passing over a pulley as shown in figure. The block $$M1$$ lies on a horizontal surface. The coefficient of friction between the block $$M1$$ and the horizontal surface is μ. The system accelerates. What additional mass m should be placed on the block $$M1$$ so that the system does not accelerate?

Infinity Learn · Accepted Answer

For the equilibrium of block of mass $$M1$$:Friction force, f $$=$$ tension in the string Twhere T $$=$$ f $$=$$ μ(m+M1)gt----------(i)For$$ the equilibrium of block of mass $$M2$$:T $$=$$ $$M2g------------(ii)From$$ $$(i) and (ii) μ$$(m+M1)g$$ $$=$$ $$M3gm$$ $$=$$ $$M2$$μ$$-M1$$

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