First slide

Connected bodies

Question

In the balance machine shown in the figure, which arm will move downward after the system is released (assuming string and the pulley to be ideal)

Moderate

A

Left
B

Right
C

Remains stationary
D

None of these

Solution

$\large T_1=2 X [\frac{2\;X\;2m\;X\;3m\;X\;g}{(2m+3m)}]$
$\large \Rightarrow T_1=\frac{24}{5}\;mg$
$\large and\;T_2=2\;X\;[\frac{2\;X\;m\;X\;4m\;X\;g}{m+4m}]$
$T_{2} = \frac{16 mg}{5}$
T₁ > T₂
$∴$ Left arm will move downward

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