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Q.

A body of mass m is projected from the surface of earth making an angle of 60o with horizontal with a speed gR where, R is the radius of earth and g is the acceleration due to gravity on the surface of earth. Then select the correct option.

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a

Angular momentum of the body about the point of projection remains conserved.

b

Angular momentum of the body about the centre of earth remain conserved and is equal to 12mgR3

c

Total energy of the body-earth system is -34mgR

d

Both (2) and (3) are right

answer is B.

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Detailed Solution

The only force acting on the body is the gravitational attraction of earth and this force always passes through the centre of earth. Therefore, gravitational force of attraction does not produce any moment about centre of earth and hence, angular momentum about centre of earth (L) remains conserved.L=m.(vcos60o).R=mgR.12.R=12mgR3Total energy =12mgR2+-GMmR=12mgR-mgR=-12mgR

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A body of mass m is projected from the surface of earth making an angle of 60o with horizontal with a speed gR where, R is the radius of earth and g is the acceleration due to gravity on the surface of earth. Then select the correct option.