A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of earth is M and its radius is R. If the magnitude of gravitational force exerted by earth on the rod is `(etaGMm)/(12R^(2))` then `eta` is

Options

A. `(GmM)/(4R^2)`
B. `(GmM)/(2R^2)`
C. `(4GMm)/(9R^2)`
D. `(GMm)/(8R^2)`

Answer

B

Explanation

`dm=(mdx)/R , dF=(GM dm)/x^2 = (GM mdx)/(Rx^2)`
`F=int_R^(2R)(GMmdx)/(Rx^2)=(GMm)/R[-1/x]_R^(2R)=(GMm)/R[-(1/(2R) 1/R)]=(GMm)/(2R^2)`