A body situated on the surface of the earth, of mass M and radius R, at its equator, becomes weightless, when the rotational kinetic energy of the earth, reaches a critical value K. The value of K is given by

Options

A. `(1)/(2)MgR`
B. `(1)/(3)MgR`
C. `(1)/(4)MgR`
D. `(1)/(5)MgR`

Answer

D

Explanation

For the body on the equator to become weightless,
`mg'=0` as `m ne 0 " " therefore g' = 0`
`therefore g'=g-R omega^(2)=0` or `omega^(2)=(g)/(R )`
For this the rotational K.E. of the earth should reach a critical value,
`K=(1)/(2)I omega^(2)=(1)/(2)xx(2)/(5)MR^(2)xx (g)/(R )=(1)/(5)MgR`