Gravitation Question 301
Question: A straight rod of length L extends from $ [x=a] $ to$ [x=L+a] $ . Find the gravitational force it exerts on a point mass m at x = 0 if the linear density of rod$ [\mu =A+Bx^{2}] $ .
Options:
A) $ [Gm\left[ \frac{A}{a}+BL \right]] $
B) $ [Gm\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]] $
C) $ [Gm\left[ BL+\frac{A}{a+L} \right]] $
D) $ [Gm\left[ BL+\frac{A}{a} \right]] $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ [\because dF=\frac{GM\left( \mu dx \right)}{x^{2}}] $ $ [F=GM\int{\left( A+Bx \right)\frac{dx}{x}}] $ $ [F=GM\left[ A\left( \frac{1}{a}-\frac{1}{a+L} \right)+BL \right]] $
