Question

A block of stone of mass 30 kg (S.G. 3) hangs from a cord and is completely immersed in water. Find the tension in the cord.

Answer 1

Given:

Stone of mass m = 30 kg and specific gravity ,=3 hangs from a cord and completely submerged in water.

To Find:

Tension in the cord

Solution:

The question is of the topic - Buoyancy

Free body diagram of stone.

1) mg downwards

2) buoyant force = $\rho Vg$ (upwards)

3) tension T(upwards)

Where p is the density of water and V is the volume displaced,

Since the stone is submerged completely hence

Volume of fluid displaced = volume of the stone.

Net force = 0

T= $mg - \rho Vg$

T = $(p_{stone}- p_{liquid})Vg$

$p_{stone} Vg = m = 30\\p_{stone } = 3000 g = 9.80\\V = .00102m^{3}$

$T = (3000-1000 ) .00102(9.80)$

T= 20 N

Tension in cord = 20 N