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 `R`. Then the magnitude of gravitational force exerted by earth on the rod is

Options

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

Answer

A

Explanation

`F=int_(R)^(2R)=(GM(m/R)dx)/(x^(2))=(GMm)/(2R^(2))`