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Net Force

A spring bala...

Question

A spring balance reads $w_{1}$ when a ball is suspended from it. A weighing machine reads $w_{2}$ when a tank containing liquid is kept on it. When the ball is immersed in the liquid, the spring balance reads $w_{3}$ and weighing machine reads $w_{4}$ . Then,

w_{1} > w_{3}

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w_{2} < w_{4}

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w_{1} + w_{2} = w_{3} + w_{4}

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w_{1} + w_{4} = w_{2} + w_{3}

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Solution

The correct options are
A $w_{1} > w_{3}$
C $w_{1} + w_{2} = w_{3} + w_{4}$
D $w_{2} < w_{4}$
When ball is immersed in liquid:
Weight $W$ will decrease due to force on the ball by the liquid.
$W_{3}$ - weight when immersed in liquid
$W_{1}$ - weight when suspended from the spring balance without being immersed in the liquid
Hence, $W_{1}$ > $W_{3}$ ....(1)
When ball is immersed in liquid reading of the weighing machine:
The ball pushes the liquid with a force to the buoyancy force in the opposite direction. this will increase the weight of the tank and the reading of the weighing machine will increase.
$W_{2}$ - reading of the weighing machine with the tank on it
$W_{4}$ - reading of the weighing machine with the ball immersed in the tank
$W_{4}$ > $W_{2}$ ....(2)
From (1) and (2) combining we get,
$W_{1} + W_{2} = W_{3} + W_{4}$ since increase in weight in one case is equal to the decrease in other case.

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