Question

An infinite line mass element has linear mass density $\lambda$. If the gravitational field at distance $r$ is $-\left(\frac{n\lambda G}{r}\right)\hat{r}$, then find the value of ${}^{\prime }{n}^{\prime }$

• A. $2$
• B. $3$
• C. $1$
• D. $4$

Answer 1

Answer: (A)

$2$

$\lambda =\frac{m}{l}\Rightarrow m=\lambda l$
Using Shell Theorem, gravitational field = $\overrightarrow{{\epsilon }_g}$
$\left|\overrightarrow{{\epsilon }_g}\right|\left(2\pi rl\right)=-4\pi Gm$
$\Rightarrow {\epsilon }_g=-\frac{2\lambda G}{r}(\therefore m=\lambda l)$
$\Rightarrow n=2$