Question

A cork has weight mg and density 25% of water’s density. A string is tied around the cork and attached to the bottom of a water-filled container. The cork is totally immersed. Express the tension in the string in terms of the cork weight mg.

Answer 1

Step-by-step explanation:

Given

Density of Cork
`\rho _c=0.25\rho _(water)`

Considering V be the volume of Cork

Buoyant Force will be acting Upward and Weight is acting Downward along with T

Since density of water is more than cork therefore Cork will try to escape out of water but due to tension it will not

we can write as

`\rho _(water)Vg-\rho _Cvg-T=0`

where T=tension

Thus Tension T is

`T=Vg(\rho _(water)-\rho _c)`

Taking
`\rho _c` common

`T=\rho _cVg((\rho _(water))/(\rho _c)-1)`

`T=mg((\rho _(water))/(\rho _c)-1)`

`T=mg(4-1)`

`T=3mg`