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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
  1. Gm[Aa+BL]
  2. Gm[BL+Aa+L]
  3. Gm[A[1a1a+L]+BL]
  4. Gm[BLa+Aa2]

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

The gravitational force is given by,
dF=Gm(λdx)x2=Gm(A+Bx2)dxx2dF=Gm(L+aaAxdx+L+aaBdx)=GmL+a[Ax]a+L+aBxa=Gm[AaAL+a+B((L+a)a)]=Gm[A(1a1L+a)+BL]

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