Question

g An object with mass m=2 kg is completely submerged, and tethered, to the bottom of a large body of water. If the density of the water is rhow = 1000 kg/m3and the density of the object is rhoob j=500 kg/m3, find the tension in the rope. Take g=10 m/s2and assume the object has a uniform mass density

Answer 1

Answer:

The tension in the rope is 20 N

Solution:

As per the question:

Mass of the object, M = 2 kg

Density of water, $\rho_{w} = 1000\ kg/m^{3}$

Density of the object, $\rho_{ob} = 500\kg/m^{3}$

Acceleration due to gravity, g = $10\ m/s^{2}$

Now,

From the fig.1:

'N' represents the Bouyant force and T represents tension in the rope.

Suppose, the volume of the block be V:

V = $\frac{M}{\rho_{ob}}$              (1)

Also, we know that Bouyant force is given by:

$N = \rho_{w}Vg$

Using eqn (1):

$N = \rho_{w}\frac{M}{\rho_{ob}}g$

$N = 1000\frac{2}{500}\times 10 = 40\ N$

From the fig.1:

N = Mg + T

40 = 2(10) + T

T = 40 - 20 = 20 N

$N = \rho_{w}Vg$