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A straight rod of length $L$ extends from $x = a$ to $x = L + a$. The gravitational force it exerts on a point mass $‘m’$ at $x = 0$, if the mass per unit length of the rod is $A + Bx^2$, is given by

• A
  $Gm\left[ {A\left( {\frac{1}{{a + L}} - \frac{1}{a}} \right) - BL} \right]$
• B
  $Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) - BL} \right]$
• C
  $Gm\left[ {A\left( {\frac{1}{{a + L}} - \frac{1}{a}} \right) + BL} \right]$
• ✓
  $Gm\left[ {A\left( {\frac{1}{a} - \frac{1}{{a + L}}} \right) + BL} \right]$