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The Simple Pulley

In the figure...

Question

In the figure, the blocks $A$ , $B$ and $C$ of mass m each have acceleration $a_{1}$ , $a_{2}$ and $a_{3}$ respectively. $F_{1}$ and $F_{2}$ are external forces of magnitude 2 mg and mg respectively. Then

A

a_{1} = a_{2} = a_{3}

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B

a_{1} > a_{3} > a_{2}

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C

a_{1} = a_{1} . > a_{2} > a_{3}

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D

a_{1} > a_{2}, a_{2} = a_{3}

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Solution

The correct option is A $a_{1} = a_{2} = a_{3}$
equation of motion of the three case are as follows-
CASE $A$
$2 m g - m g = m a_{1}$
$\Rightarrow$ $a_{1} = g$
CASE $B$
$T - m g = m a_{2}$
$2 m g - T = 2 m a_{2}$
$\Rightarrow$ $a_{2} = \frac{g}{3}$
CASE $C$
$T - m g = m a_{3}$
$m g + m g - T = m a_{3}$
$\Rightarrow$ $a_{3} = \frac{g}{2}$ .

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Similar questions

Q. In the figure, the blocks

A, B

C

m

each have acceleration

a_{1}, a_{2}

a_{3}

F_{1}

F_{2}

are external forces of magnitudes

2 m g

each. What is the relation between the acceleration of the masses

A

B

C

a_{1}, a_{2}, a_{3}, . . . a_{n}

are in H.P then

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . a_{n}}, \frac{a_{3}}{a_{1} + a_{2} + a_{4} + . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n}}

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1}, a_{2}, a_{3}, . . . . a_{n}

are in H.P, then

\frac{a_{1}}{a_{2} + a_{3} + . . . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, . . . ., \frac{a_{n}}{a_{1} + a_{2} + . . . . + a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . . a_{n}

are in H.P., then

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n - 1}}

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