1. Tardigrade
  2. Question
  3. Physics
  4. A body is fired with a 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:

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Q. A body is fired with a velocity of magnitude $\sqrt{gR} < V < \sqrt{2gR}$ 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:

Gravitation

Solution:

Conservation of angular momentum of the body about $O$ yields
image
$(mV\,sin\,30^{\circ} )R = 2V'(R + h)$
$\frac{V}{2}R = \frac{V}{4} (R + h)[\therefore V' = \frac{V}{4}]$
$\therefore h = R$