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Density

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 of liquid is kept on it. When the ball is immersed in the liquid, the spring balance reads $W_{3}$ and the weighing machine reads $W_{4}$ .

W_{1} > W_{3}

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W_{1} < W_{3}

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W_{2} < W_{4}

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W_{2} > W_{4}

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Solution

The correct options are
A $W_{1} > W_{3}$
C $W_{2} < W_{4}$
Using Spring Balance:
When the ball is immersed in the liquid, upward thrust will be there on the ball. Hence, $W_{3}$ recorded by the spring balance is less than $W_{1}$ recorded by the spring balance when the ball is not immersed in the liquid.
$W_{3} < W_{1}$
When using Weighing machine:
The ball will provide a downward force( equal to buoyancy force B) on the liquid when the ball is immersed in the liquid. The reading of weighing machine will be the normal reaction provided by the machine.
$N = W_{4} = B + W_{2}$
$\Rightarrow W_{4} > W_{2}$ ie $W_{2} < W_{4}$

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