A body is fired with a velocity of magnitude √gR

Question

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: (A) V2/8g (B) R (C) √2R (D) none of these

Tardigrade Admin · Accepted Answer

Conservation of angular momentum of the body about O yields <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/74f0fa6b34a4276bafd8fb932d14cf85-.png" /> (mV sin 30° )R = 2V'(R + h) (V/2)R = (V/4) (R + h)[∴ V' = (V/4)] ∴ h = R

Q. A body is fired with a velocity of magnitude $g R < V < 2 g R$ at an angle of $3 0^{\circ}$ 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:

$V^{2} /8 g$

$R$

$2 R$

none of these

Conservation of angular momentum of the body about $O$ yields

$(mV s in 3 0^{\circ}) R = 2 V^{'} (R + h)$

$\frac{V}{2} R = \frac{V}{4} (R + h) [∴ V^{'} = \frac{V}{4}]$

$∴ h = R$

Q. 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:

V2/8g

R

2​R

none of these

Conservation of angular momentum of the body about O yields (mVsin30∘)R=2V′(R+h) 2V​R=4V​(R+h)[∴V′=4V​] ∴h=R

Q. A body is fired with a velocity of magnitude $g R < V < 2 g R$ at an angle of $3 0^{\circ}$ 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:

$V^{2} /8 g$

$R$

$2 R$

Conservation of angular momentum of the body about $O$ yields

$(mV s in 3 0^{\circ}) R = 2 V^{'} (R + h)$

$\frac{V}{2} R = \frac{V}{4} (R + h) [∴ V^{'} = \frac{V}{4}]$

$∴ h = R$