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.

Options

A. `(4GMm)/((a+l)^(2))`
B. `(4GmM)/(4a^(2)-l^(2))`
C. `(GMm)/(a^(2))`
D. `(GmM)/(2(l+a)^(2))`

Answer

B

Explanation

`dF=(GmdM)/(x^(2))`
`:. F=int_(x=a)^(x=a+1)dF`
`=int_(a-l//2)^(a+l)(G.m((M)/(l).dx))/(x^(2))=(4Gm M)/(4a^(2)-l^(2))`