Q111 / 200 · NEET 2023 (All India) · Physics

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

A
$- \frac{20 G m}{R}$
B
$- \frac{8 G m}{R}$
C
$- \frac{12 G m}{R}$
Correct answer
D
$- \frac{16 G m}{R}$

Solution

Let the gravitational field at point $Q$ is zero. Therefore, we can write
$(\frac{- G m}{x^{2}}) + (\frac{- G \times 9 m}{{(R - x)}^{2}}) = 0 \Rightarrow \frac{{(R - x)}^{2}}{x^{2}} = 9 \Rightarrow x = \frac{R}{4}$
Now, net gravitational potential at point $Q$ will be
$V_{n e t} = (\frac{- G m}{x}) + (\frac{- G \times 9 m}{R - x}) = (\frac{- G m}{\frac{R}{4}}) + (\frac{- G \times 9 m}{\frac{3 R}{4}}) = \frac{- 16 G m}{R}$

Hence, the correct answer is option: 'D'.

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

Solution

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