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  • A body is fired with velocity of magnitude <img alt="\mathrm{\sqrt{\mathrm{gR}}<v<\sqrt{2 \mathrm{gR}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Csqrt%7B%5Cmathrm%7

A body is fired with velocity of magnitude \mathrm{\sqrt{\mathrm{gR}}<v<\sqrt{2 \mathrm{gR}}} at an angle of 30^{\circ} 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

Option: 1

\mathrm{v^2 / 8 g}


Option: 2

R


Option: 3

\mathrm{\sqrt{2} R}


Option: 4

none of these


Answers (1)

best_answer

Conservation of angular momentum of the body about O yields

\mathrm{\begin{aligned} & m v(\sin 30) R=m v^{\prime}(R+h) \\ & \Rightarrow \frac{v}{2} R=\frac{v}{4}(R+h) \Rightarrow h=R . \end{aligned}}

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Rishabh

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