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Question

# A straight rod of length L extends frfom x=a to x=L+a. Find the gravitational force it exerts on a point mass m at x=0 is(if the linear density of rod μ=A+Bx2)

A
Gm[Aa+BL]
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B
Gm[A(1a1a+L)+BL]
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C
Gm[BL+Aa+L]
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D
Gm[BLAa]
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Solution

## The correct option is B Gm[A(1a−1a+L)+BL]Let us consider the gravitational force between the point mass and a small element of rod located at a distance x from the massdF=Gm(μdx)x2Total force between them will be the integral of above equation∫dF=Gm∫L+aa(A+Bx2)dxx2F=Gm[−A1x+Bx]L+AaF=Gm[−A(1L+a−1a)+B(L+a−a)]F=Gm[A(1a−1L+a)+BL]

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