A body is fired with velocity of magnitude √gR< V< √2gR at an angle of 30° with the radius vector of earth. If at the highest point the speed of the body is v/4 , the maximum height attained by the body is equal to

Q: A body is fired with velocity of magnitude √gR< V<√2gR  at an angle of 30° with the radius vector of earth. If at the highest point the speed of the body is v/4, the maximum height attained by the body is equal to
(A) v²/8g
(B) R
(C) √2 R
(D) none of these
where R = radius of earth. (Use the appropriate assumptions)
Solution :
Gravitation
Conservation of angular momentum of the body about O yields
mv (sin30°) R = mv'(R + h)
½ vR = ¼ v(R + h)
Hence , h = R.

Author: Rajesh Jha

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