Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position were the gravitational field due to them is zero is

Question

Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position were the gravitational field due to them is zero is (A) V=(G/d)(m+M) (B) V=(Gm/d) (C) V=(GM/d) (D) V=(G/d)(√m+√M)2

Tardigrade Admin · Accepted Answer

If net gravitational field of p becomes zero means

\frac{G m}{x ^{2}} = \frac{GM}{( d - x ) ^{2}} \Rightarrow x = \frac{( m ) d}{m + M}

and

d - x = \frac{( M ) d}{m + M}

Gravitational potential at

\frac{- G m}{\frac{( m ) d}{m + M}} + \frac{- G m}{\frac{( M ) d}{m + M}} = - \frac{G}{d} (m + M)^{2}

Q. Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position were the gravitational field due to them is zero is

$V = \frac{G}{d} (m + M)$

$V = \frac{G m}{d}$

$V = \frac{GM}{d}$

$V = \frac{G}{d} (m + M)^{2}$

Q. Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position were the gravitational field due to them is zero is

V=dG​(m+M)

V=dGm​

V=dGM​

V=dG​(m​+M​)2

If net gravitational field of p becomes zero means x2Gm​=(d−x)2GM​⇒x=m​+M​(m​)d​ and d−x=m​+M​(M​)d​ Gravitational potential at m​+M​(m​)d​−Gm​+m​+M​(M​)d​−Gm​=−dG​(m​+M​)2

$V = \frac{G}{d} (m + M)$

$V = \frac{G m}{d}$

$V = \frac{GM}{d}$

$V = \frac{G}{d} (m + M)^{2}$