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Question

# A straight rod of length L, extends from x=a to x=L+a. The linear mass density of the rod varies with x- coordinate is λ=A+Bx2. The gravitational force experienced by a point mass m at x=0 is

A
Gm[Aa+BL]
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B
Gm[BL+Aa+L]
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C
Gm[A[1a1a+L]+BL]
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D
Gm[BLa+Aa2]
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Solution

## The correct option is C Gm[A[1a−1a+L]+BL]Force experienced by m at x=0 due to a small mass dm of rod at x=x is given by : dF=Gmdmx2 (AsF=GMmr2) Now dm=λdx=(A+Bx2)dx F=∫L+aaGm(A+Bx2)dxx2 ⇒F=Gm(A∫L+aa1x2dx+B∫L+aax2x2) ⇒F=Gm(A−1L+axa+BxL+aa) ⇒F=Gm(A(1a−1a+L)+BL)

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