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A mass m is at a distance a from one end...

A mass m is at a distance a from one end of a uniform rod of length l and mass M. Find the gravitational force on the mass due to the rod.

A

`(GM^(2))/(L^(2))`

B

`(GM^(2))/(2L^(2))`

C

`(2GM^(2))/(3L^(2))`

D

`(4GM^(2))/(9L^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Consider an element of the rod of length `dx` at adistance `x` from point mass as shown in Fig.

Mass of element `= (M//L)dx`
Force experienced by point mass due to this
element is `dF = (GM xx (M//L) dx)/(x^(2)) = (GM^(2))/(L) (dx)/(x^(2))`
Total force experienced by point mass due to whole
rod is `F = int_(L)^(2L) (GM^(2))/(L) (dx)/(r^(2)) = (GM^(2))/(2L^(2))`
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