Question

A piece of cork (density 250 kg/m3 ) of mass 0.01 kg is held in place under water (density 1000 kg/m3 ) by a string. What is the tension, T, in the string? [Use g = 10 m/s2 ]

Answer 1

Tension = 0.3 N

Step-by-step explanation:

As we know that the cork is inside water

so the buoyancy force on the cork is counter balanced by tension force in string and weight of the block

So the force equation is given as

`F_b = T + mg`

now we will have

`Volume = (mass)/(density)`

`V = (0.01)/(250) = 4 * 10^(-5) m^3`

now buoyancy force on the block is given by

`F_b = \rho V g`

`F_b = 1000(4 * 10^(-5))(10)`

`F_b = 0.4 N`

now by force balance equation

`0.4 = T + 0.01(10)`

`T = 0.4 - 0.1 = 0.3 N`

Answer 2

0.3 N

Step-by-step explanation:

mass of cork = 0.01 kg, density of cork = 250 kg/m^3

density of water = 1000 kg/m^3, g = 10 m/s^2

Tension in the rope = Buoyant force acting on the cork - Weight of the cork

Buoyant force = volume of cork x density of water x g

= mass x density of water x g / density of cork

= 0.01 x 1000 x 10 / 250 = 0.4 N

Weight of cork = mass of cork x g = 0.01 x 10 = 0.1 N

Thus, the tension in the rope = 0.4 - 0.1 = 0.3 N