If the earth suddenly charges its radius x times the present value, the new period of rotation would be

Options

A. `6x^(2)h`
B. `12x^(2)h`
C. `24x^(2)h`
D. `48x^(2)h`

Answer

C

Explanation

As, no torque is applied, angular momentum will be conserved.
`L=l omega="constant"=((2)/(5)MR^(2))((2pi)/(T))="constant i.e."`
`rArr" "(R^(2))/(T)="constant"`
`rArr" "(R_(1)^(2))/(T_(1))=(R_(2)^(2))/(T_(2))`
`therefore" "T_(2)=(R_(2)^(2))/(R_(1)^(2))T_(1)=((xR_(1))/(R_(1)))^(2)xx24A`
`=24x^(2)h`