Gravitation

JEE Main level, single correct, medium

157 of 223

Question 157 of 223

Two bodies of masses m\mathrm{m} and 4 m4 \mathrm{~m} are placed at a distance r\mathrm{r}. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

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Answer: (C) −9Gmr-\frac{9 \mathrm{Gm}}{r}

Position of the null point from mass m,x=r1+4 m m=r3\mathrm{m}, \mathrm{x}=\frac{\mathrm{r}}{1+\sqrt{\frac{4 \mathrm{~m}}{\mathrm{~m}}}}=\frac{r}{3}
V=−Gm(3r+122r)=−9GmrV=-G m\left(\frac{3}{r}+\frac{12}{2 r}\right)=-9 \frac{G m}{r}

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