The mass of the earth is increasing at the rate 1 part in `5 xx 20^(19)` per day by the accretion of meteors falling normally upon the earth's surface. Find the corresponding rate of change of the period of rotation of the earth supporting the earth to be a sphere of uniform density.
[Hint: Consider the deposit as a spherical shell and apply principle of conservation of angular momentum]

Options

A. `2.0xx10^(-30)`
B. `2.66xx10^(-19)`
C. `4.33xx10^(-18)`
D. `5.66xx10^(-17)`

Answer

A

Explanation

As angular momentum is conserved in the absence of a torque, therefore `l_(0)omega_(0)=l omega`
`((2)/(3)MR^(2))((2pi)/(T_(0)))=[(2)/(5)MR^(2)+(2)/(5)(MR^(2))/(5xx10^(19))](2pi)/(T)`
`(T)/(T_(0))=1+(1)/(5xx10^(19))rArr (T)/(T_(0))-1=(1)/(5xx10^(19))=2xx10^(-20)`