1.Plaskett's binary system consists of two stars that revolve in a circular orbit about a centre of gravity midway between them.This means that the masses of the two stars are equal if the orbital speed of each star is V and the orbital period of each is T, find the mass M of each star.
2. A projectile is launched from the surface of the earth with a very high speed V at an angle ∂ with vertical.what is its velocitywhen it is at the farthest distance from the earth surface given that the Maximum height reached by the projectile is equal to the height reached when it is launched perpendicular to the surface with a velocity equal to √GM/R
a) Vcos∂2
b) Vsin∂/2
c) √GM/2R
d) √GM/3R
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3 Answers
49in 2nd one we have to consider the change in gravitational force of attraction on increasing distances...[1]
49in first one actually indirectly radius of rotation is given indirectly through time period...velocity is given...we have to find out mass by balancing forces..[1][1]
49time taken for 1 full revolution=T
tangential velocity =V...constant..
thus at any time of revolution the speed=V
thus total distance covered in 1 revolution=VT=2Ï€R
=> R=VT/2Ï€
now, GMM/(2R)2=MV2/R
or, GM/4R=V2
or, M=4RV2/G...[1][1]
