- Home
- Standard 11
- Physics
7.Gravitation
hard
A particle is projected from the mid - point of the line joining two fixed particles each of mass $'m$'. If the separation between fixed particles is $'l$', the minimum velocity of projection of the particle so as to escape is equal to
A
$\sqrt {\frac{{Gm}}{l}}$
B
$\sqrt {\frac{{Gm}}{2l}}$
C
$\sqrt {\frac{{2Gm}}{l}}$
D
$2\sqrt {\frac{{2Gm}}{l}}$
Solution
Gravitational potential energy
$= \frac {-4Gmm_{0}}{\ell}$
to escape, $\Delta \mathrm{KE}+\Delta \mathrm{PE}=0$
$=\left(0-\frac{1}{2} m_{0} v^{2}\right)+\left\{0-\left(-\frac{4 G m m_{0}}{\ell}\right)\right\}=0$
$v=2 \sqrt{\frac{2 G m}{\ell}}$
Standard 11
Physics
