171.
Three equal masses (each $$m$$) are placed at the comers of an equilateral triangle of side $$'a'.$$ Then the escape velocity of an object from the circumcentre $$P$$ of triangle is :
A
$$\sqrt {\frac{{2\sqrt 3 Gm}}{a}} $$
B
$$\sqrt {\frac{{\sqrt 3 Gm}}{a}} $$
C
$$\sqrt {\frac{{6\sqrt 3 Gm}}{a}} $$
D
$$\sqrt {\frac{{3\sqrt 3 Gm}}{a}} $$
Answer :
$$\sqrt {\frac{{6\sqrt 3 Gm}}{a}} $$
172. In planetary motion the areal velocity of position vector of a planet depends on angular velocity $$\left( \omega \right)$$ and the distance of the planet from sun $$\left( r \right).$$ If so, the correct relation for areal velocity is
A
$$\frac{{dA}}{{dt}} \propto \omega r$$
B
$$\frac{{dA}}{{dt}} \propto {\omega ^2}r$$
C
$$\frac{{dA}}{{dt}} \propto \omega {r^2}$$
D
$$\frac{{dA}}{{dt}} \propto \sqrt {\omega r} $$
Answer :
$$\frac{{dA}}{{dt}} \propto \omega {r^2}$$