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Question

# Two blocks of masses M1 and M2 are connected with a string passing over a pulley as shown in the 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?

A
M2M1μ
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B
M2μM1
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C
M2M1μ
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D
(M2M1)μ
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Solution

## The correct option is B M2μ−M1For the system to be in equilibrium: For block of mass M1: Frictional force, f= tension in the string, T where f=μ(m+M1)g ... (1) ∴T=μ(m+M1)g ... (2) For the equilibrium of block of mass M2: T=M2g ... (3) Hence, μ(m+M1)g=M2g ∴m=M2μ−M1 Hence, the correct answer is option (b).

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