JEE PHYSICS MCQ: GRAVITATION

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Six stars of equal mass

m

are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. Their common time period of revolution around center will be

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Correct option: B

2 \pi \sqrt{\frac{4 \sqrt{3} a^3}{G m(5 \sqrt{3}+4)}}

Option B is correct because the time period is derived by equating the centripetal force on each star to the net gravitational force due to the other stars in the hexagonal arrangement.

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The escape velocity for a body projected vertically upwards from the surface of the earth is

11.2\mathrm{\;\;km}{\mathrm{s}^{ - 1}}

. If the body is projected in a direction making an angle of

{45^0}

with the vertical, the escape velocity will be The escape velocity of a body projected from the surface of earth is

v_e

. If the body is projected at an angle

\theta

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