Two spheres of volume 250 cc each but of relative densities 0.8 an d 1.2 are connected by a string and the combination is immersed in a liquid. Find the tension T in the string. `(g=10m//s^(2))`

Explanation

The tension on denser sphere is upwards and on lighter sphere is downwards.

`V_(b_(1))rho_(1)g+T=V_(b_(1))rho_(l)g`
`therefore (250xx10^(-6)xx800g)+T=250xx10^(-6)xxrho_("liquid")g-(i)`
`V_(b_(2))rho_(2)g-T=V_(b_(2))rho_(l)g`
`(250xx10^(-6)xx1200g)-T=250xx10^(-6)xxrho_("liquid")g-(ii)`
subtract Eqs. (ii) from (i), we get
`2T=250xx10^(-6)xx400 grArr T=0.5N`