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Spring 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 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 $W_{4}$ . Then, which of the following are not correct?

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 option is D $W_{2} > W_{4}$
Let us try to understand all the situation with the help of diagrams below
In case 1: Only weight of the ball is measured i.e $W_{1}$
In case 3: Weight of the ball is measured i.e $W_{3}$ when buoyancy force is acting on the ball which will try to lift the ball so,
$W_{3} < W_{1}$
In case 2: The weight of the water tank is measured $W_{2}$
In case 4: Weight of the water tank and the ball both are getting measured. The weight of the ball is less as discussed in case 3.
$W_{4} > W_{2}$ ( $∵$ weight of ball is getting added up to $W_{4}$ )
So, option 1 and 4 are correct.
But in question they asked the options which are not correct so, B and D are correct options for this question.

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