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A uniform thin rod of mass m and length ...

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

A

`(GmM)/(4R^2)`

B

`(GmM)/(2R^2)`

C

`(4GMm)/(9R^2)`

D

`(GMm)/(8R^2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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