Two bodies of mass m and 9m are placed at a distance of R. T... | Physics | SolveeIt

Question

Two bodies of mass m and 9m are placed at a distance of R. The gravitational potential on the line joining the bodies where the gravitational fied equals zero, will be (G = gravitational contant):

$-\frac{20 Gm}{R}$

$-\frac{8Gm}{R}$

$-\frac{12Gm}{R}$

$-\frac{16Gm}{R}$

Answer

$-\frac{16Gm}{R}$

Explanation

Solution

Position of netural point
position of neutral point(zero gravitational field)
$r_1=\frac{\sqrt(m_1)R}{\sqrt{m_1+\sqrt{m+2}}}=\frac{\sqrt{m}R}{\sqrt m+\sqrt{9m}}=\frac{R}{4}$
$r_2=R-\frac{R}{4}=\frac{3R}{4}$
Now gravitational potential at point P
$V_p=-\frac{GM}{\frac{R}{4}}-\frac{9GM}{\frac{3R}{4}}$
$=-\frac{16GM}{R}$
Therefore, the correct option is (D) : $-\frac{16Gm}{R}$ .

Physics Question on Gravitation

Solution