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,

A
w1>w3
B
w2<w4
C
w1+w2=w3+w4
D
w1+w4=w2+w3

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 liquidHence, $$W_1$$ > $$W_3$$  ....(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.Physics

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