Question

The spring balance A reads 2kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation:

• A. The balance A will read more than 2 kg
• B. The balance B will read more than 5 kg
• C. The balance A will read less than 2 kg and B will read more than 5 kg
• D. The balance A and B will read 2 kg and 5 kg respectively

Answer 1

The correct option is C

The balance A will read less than 2 kg and B will read more than 5 kg

$F_s$ = spring force

$F_B$ = Buoyant force

Free body diagram of block

As it is an equilibrium, $mg=F_s+F_B$

$\Rightarrow F_s=mg-F_B$ - - - - - - (1)

Free body diagram of the container with liquid

As mentioned the block will apply an equal and opposite buoyant force on the water which in turn will apply the force on the container as it is incompressible.

Due to equilibrium,

$N=Mg+F_B$ - - - - - - (2)

From now we can see that the weight measured by the spring balance will be $F_s$ and N will be the weight measured by the weighing machine.

From (1) and (2) we can see that the balance A will read less than 2 kg and B will read more than 5 kg as we know mg = 2 kg and Mg = 5 kg.