Question

Two point masses having mass $m$ and $2m$ are placed at distance $d$. The point on the line joining point masses, where gravitational field intensity is zero will be at distance:

• A. $\frac{2d}{\sqrt{3}+1}$ from point mass ${}^{\prime \prime }2m^{\prime \prime }$
• B. $\frac{2d}{\sqrt{3}-1}$ from point mass ${}^{\prime \prime }2m^{\prime \prime }$
• C. $\frac{d}{1+\sqrt{2}}$ from point mass ${}^{\prime \prime }{m}^{\prime \prime }$
• D. $\frac{d}{1-\sqrt{2}}$ from point mass ${}^{\prime \prime }{m}^{\prime \prime }$

Answer 1

The correct option is C $\frac{d}{1+\sqrt{2}}$ from point mass ${}^{\prime \prime }{m}^{\prime \prime }$

Gravitational field Intensity,

$\frac{GM}{x^2}=\frac{G.2m}{{(d-x)}^2}$

$\Rightarrow \frac{{(d-x)}^2}{x^2}=2$

$\Rightarrow \frac{d-x}{x}=\sqrt{2}$

$\Rightarrow d=\sqrt{2}x+x$

$\Rightarrow d=x(\sqrt{2}+1)$

$x=\frac{d}{\sqrt{2}+1}$ from mass $M$ [option C].