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Standard XI

Physics

Pulley

Two masses m1...

Question

Two masses $m_{1} a n d m_{2}$ which are connected with a light string, are placed over a frictionless pulley. This set up is placed over a weighing machine, as shown. Three combination of masses $m_{1} a n d m_{2}$ are used, in first case $m_{1} = 6 k g a n d m_{2} = 2 k g,$ In second case $m_{1} = 5 k g a n d m_{2} = 3 k g$ and in third case $m_{1} = 4 k g a n d m_{2} = 4 k g .$ Masses are held stationary initially and then released. If the readings of the weighing machine after the release in three cases are $W_{1}, W_{2} a n d W_{3}$ respectively then:

W_{1} > W_{2} > W_{3}

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W_{1} < W_{2} < W_{3}

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W_{1} = W_{2} = W_{3}

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W_{1} = W_{2} < W_{3}

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Solution

The correct option is B $W_{1} < W_{2} < W_{3}$

Reading of the weighing machine $= 2 T +$ weight of the assembly.
As weight of the assembly is constant $T = \frac{2 m_{1} m_{2}}{m_{1} + m_{2}}$
So reading is maximum for the case $m_{1} m_{2}$ is maximum as $m_{1} + m_{2}$ in all cases is same.

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Q. Two masses

m_{1}

and

m_{2}

which are connected with a light string are placed over a frictionless pulley. This set up is placed over a weighing machine as shown in figure. Three combination of masses

m_{1}

and

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are used, in first case

m_{1} = 6 kg

and

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, in second case

m_{1} = 5 kg

and

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, in the third case

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. Masses are released from rest. If

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Q. Two masses

m_{1} a n d m_{2}

which are connected with a light string, are placed over a frictionless pulley. This set up is placed over a weighing machine, as shown. Three combination of masses

m_{1} a n d m_{2}

are used, in first case

m_{1} = 6 k g a n d m_{2} = 2 k g,

In second case

m_{1} = 5 k g a n d m_{2} = 3 k g

and in third case

m_{1} = 4 k g a n d m_{2} = 4 k g .

Masses are held stationary initially and then released. If the readings of the weighing machine after the release in three cases are

W_{1}, W_{2} a n d W_{3}

respectively then:

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?