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Question

A spring balance reads W1, when a ball is suspended from it. A weighing machine reads W2, when a tank of liquid is kept on it. When the ball is immersed in the liquid, the spring balance reads W3 and the weighing machine reads W4. Which of the following relationship is correct.

A
W1+W2=W3+W4
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B
W1+W3=W2+W4
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C
W1+W4=W2+W3
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D
W1+W2+W3=W4
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Solution

The correct option is A W1+W2=W3+W4
Let mass of ball be m, mass of tank be M, Buoyancy force by liquid in tank on the ball be B, k be spring constant, x1 be elongation of spring when ball is suspended in air, and x2 be elongation of spring when ball is suspended immersed in liquid.
W1=kx1=mg
W2=Mg is normal force by weighing machine.
W3=kx2=mgB
W4=mgkx2+Mg is normal force by weighing machine.
So, W1+W2=W3+W4=mg+Mg

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