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Pseudo Force

In the figure...

Question

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

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

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

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

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

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Solution

The correct option is B $a_{1} > a_{3} > a_{2}$
Equation of motion for the fiven three cases are-
case A
$2 m g - m g = m a_{1}$
$\Rightarrow a_{1} = g$
case B
$T - m g = m a_{2}$ (where T is the tension in string)
$2 m g - T = 2 m a_{2}$
$\Rightarrow a_{2} = \frac{g}{3}$
case C
$T - m g = m a_{3}$ (where T is the tension in string)
$3 m g - T = m a_{3}$
$\Rightarrow a_{3} = g$
which shows that
$a_{1} = a_{3} > a_{2}$

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If A₁, A₂, A₃,..., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then

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