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Question: Two blocks of mass \(M _ { 1 }\) and \(M _ { 2 }\) are connected with a string passing over a pu...

Two blocks of mass M1M _ { 1 } and M2M _ { 2 } are connected with a string passing over a pulley as shown in the figure. The block M1M _ { 1 } lies on a horizontal surface. The coefficient of friction between the block M1 and horizontal surface is μ. The system accelerates. What additional mass m should be placed on the block M1M _ { 1 } so that the system does not accelerate

A

M2−M1μ\frac { M _ { 2 } - M _ { 1 } } { \mu }

B

M2μ−M1\frac { M _ { 2 } } { \mu } - M _ { 1 }

C

M2−M1μM _ { 2 } - \frac { M _ { 1 } } { \mu }

D

(M2−M1)μ\left( M _ { 2 } - M _ { 1 } \right) \mu

Answer

M2μ−M1\frac { M _ { 2 } } { \mu } - M _ { 1 }

Explanation

Solution

By comparing the given condition with general expression

μ=M2m+M1\mu = \frac { M _ { 2 } } { m + M _ { 1 } } ⇒ m+M1=M2μm + M _ { 1 } = \frac { M _ { 2 } } { \mu } ⇒ m=M2μ−M1m = \frac { M _ { 2 } } { \mu } - M _ { 1 }