Two blocks of masses $M_{1} = 4 k g$ and $M_{2} = 6 k g$ are connected by a string of negligible mass passing over a frictionless pulley as shown in the figure below. The coefficient of friction between the block $M_{1}$ and the horizontal surface is $0.4$ . When the system is released the masses $M_{1}$ and $M_{2}$ start accelerating. What additional mass $m$ should be placed over $M_{1}$ so that the masses $(M_{1} + m)$ slide with a uniform speed?

12 k g

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11 k g

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10 k g

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9 k g

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Solution

The correct option is B $11 k g$
For a body to move with uniform velocity the net external force on it must be zero.
Fractional force= $M_{2} g$
$(M_{1} + m) g μ = M_{2} g$
$(4 + m) 4 = 60$
$m = 11 k g$

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Two blocks of masses $m_{1} = 4 k g$ and $m_{2} = 6 k g$ are connected by a string of negligible mass passing over a frictionless pulley as shown in the figure. The coefficient of friction between block $m_{1}$ and the horizontal surface is 0.4. When the system is released, the masses $m_{1} a n d m_{2}$ start accelerating. What additional mass $m$ should be placed over mass $m_{1}$ so that the masses $(m_{1} + m)$ slide with a uniform speed?