Question

Three identical blocks each of mass m = 1 $kg$ and volume $3\times {10}^{-4}{m}^3$ are suspended by massless strings from a support as shown. Underneath are three identical containers containing the same amount of water that are placed over the scales. In figure (a), the block is completely out of the water, in figure (b), the block is completely submerged but not touching the beaker and in figure (c), the block rests on the bottom of the beaker. The scale in figure (a) reads 14 $N$. (Take density of water 1000 $\frac{kg}{m^3}$).

• A. The tension in the string in (b) is 10 $N$.
• B. The tension in the string in (b) is 7 $N$.
• C. The reading of the scale in (b) is 17 $N$.
• D. The reading of the scale in (c) is 24 $N$.

Answer 1

Answer: (B), (C), (D)

The correct options are
B The tension in the string in (b) is 7 $N$.
C The reading of the scale in (b) is 17 $N$.
D The reading of the scale in (c) is 24 $N$.

Density of the block, $=\frac{1}{3\times {10}^{-4}}kg/m^3=\frac{10}{3}\times {10}^{3}kg/m^3$
Tension in string for figure (b) is,
$T+F_b=mg$
$T=mg-{\rho }_{w}gV=1\times 10-1000\times 10\times 3\times {10}^{-4}=7N$
$\because$ Water exert $3N$ on block as buoyant force, block also exert reaction on water equals to 3 $N$.
Hence, reading of scale in figure (b) is,
14+3= 17 $N$
In figure (c) block is at rest on the bottom surface of beaker, so tension in string is zero.
Hence reading is the combined weight of containers and block which is 10 + 14 = 24 $N$