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Standard XI

Physics

Calculating Friction Using Coeffcients

Two blocks of...

Question

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?

9 kg

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10 kg

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11 kg

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12 kg

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Solution

The correct option is C
11 kg

For the system to move with a uniform speed, net force on each block should be zero.
$T = m_{2} g$
Also, $T = f = μ (m_{1} + m) g \Rightarrow m_{2} g = μ (m_{1} + m) g \Rightarrow m_{2} = μ (m_{1} + m) \Rightarrow 6 = 0.4 (4 + m) \Rightarrow m = 11 k g$
Hence, the correct choice is (c).

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Q. Two blocks of masses

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and

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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

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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?