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A double star is a system of two stars of masses and , rotating about their centre of mass only under their mutual gravitational attraction. If is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to :
(a)
(b)
(c)
(d)

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Important Questions on Gravitation
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A solid sphere of uniform density and radius 4 units is located with its centre at the origin of coordinates. Two spheres of equal radii 1 unit, with their centres at and respectively, are taken out of the solid leaving behind spherical cavities as shown in figure. Then :-

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JEE Main/Advance
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A small ball of mass ' ' is released at a height ' ' above the Earth surface, as shown in the figure. If the maximum depth of the hall to which it goes is inside the Earth through a narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring constant and natural length , the value of is is radius of Earth and mass of Earth)

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