First slide
Static friction
Question

Two blocks of mass M1 and M2 are connected with a string passing over a pulley as shown in fig.

The block M1 lies on a horizontal surface. The coefficient of fiction between the block M and the horizontal surface is µ. The system  accelerates. What additional mass m so that the system does not accelerate ?

Moderate
Solution

The motion will stop when the force of friction is equal to the weight of M2. Thus 

 M2g=μ(M1+m)gorM2g=μm1g+μmgor M2μM1=μmm=(M2μM1)

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