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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 kg and $m_{2}$ $=$ 2 kg, in second case $m_{1}$ $=$ 5 kg and $m_{2}$ $=$ 3kg and in third case $m_{1}$ $=$ 4 kg and $m_{2}$ $=$ 4 kg. 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

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is B $W_{1} < W_{2} < W_{3}$
Answer is B
Net weight showing in the weighing machine will be equal to the tension in string on both sides i.e. on the side of $m_{1}$ and $m_{2}$ .
Therefore, W= 2T
Now, from the block diagram,
$m_{1} g - T = m_{1} a$
$T - m_{2} g = m_{2} a$
Therefore,
$2 T = \frac{m_{1} m_{2}}{m_{1} + m_{2}} g$
Now,
$W_{1} = \frac{2 X_{6} X_{2}}{6 + 2} g = 3 g$
$W_{2} = \frac{2 X_{5} X_{3}}{5 + 3} g = 3.75 g$
$W_{3} = \frac{2 X_{4} X_{4}}{4 + 4} g = 4 g$
Therefore,
$W_{1} < W_{2} < W_{3}$

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Similar questions

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,

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:

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,

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:

m_{1}

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}

m_{2}

are used, in first case

m_{1} = 6 kg

m_{2} = 2 kg

, in second case

m_{1} = 5 kg

m_{2} = 3 kg

, in the third case

m_{1} = 4 kg

m_{2} = 4 kg

. Masses are released from rest. If

W_{1}, W_{2}

W_{3}

be the reading of weighing machine in three cases, then:

Q. If W1, W2 and W3 represents the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3.

Q. A given mass of gas expands reversibly from state A to state B by three paths 1,2 and 3 as shown in the figure. If

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

respectively are the work done by the gas along three paths, then:

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