question_answer

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 \[A+B{{x}^{2}},\], is given by-               [JEE Main 12-Jan-2019 Morning]

A) \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)-BL \right]\]

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

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

D) \[Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]\]

Correct Answer: D Solution : [d]