Two small balls of same size and masses $m_{1}$ and $m_{2}$ $(m_{1} m_{2})$ are tied by a thin weightless thread and dropped from a certain height. Training upward buoyancy force $F$ into account, the tension $T$ of the thread during the flight after the motion of the ball becomes uniform will be

Question

Two small balls of same size and masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied by a thin weightless thread and dropped from a certain height. Training upward buoyancy force $F$ into account, the tension $T$ of the thread during the flight after the motion of the ball becomes uniform will be

Dr. Abubacker · Accepted Answer

(b) As both the balls are of same size, force of buoyancy on each is same. Therefore, in equilibrium,
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$F + F = m_{1}g + m_{2}g$ or $F = \left( m_{1} + m_{2} \right)\frac{g}{2}$
Considering the equilibrium of lower ball,
$T + F = m_{1}g$
$T = m_{1}g - F$
$T = m_{1}g - \left( m_{1} + m_{2} \right)\frac{g}{2}$
$T = \left( m_{1} - m_{2} \right)\frac{g}{2}$

Explanation

Reviewed by Dr. Abubacker

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