A body which is initially at rest at a height | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $M$ be the mass of the earth and $R$ be its radius. The body of mass $m$ is initially at a height $R$ above the surface,so its distance from t

Vedclass · Accepted Answer

$\sqrt{ gR }$

Vedclass · Answer

(B) Let $M$ be the mass of the earth and $R$ be its radius. The body of mass $m$ is initially at a height $R$ above the surface,so its distance from the center of the earth is $r_A = R + R = 2R$.Using the Law of Conservation of Mechanical Energy between point $A$ (at height $R$) and point $B$ (at the surface):$E_A = E_B$$K_A + U_A = K_B + U_B$Since the body is initially at rest,$K_A = 0$.$0 - \frac{G M m}{2R} = \frac{1}{2} m v^2 - \frac{G M m}{R}$$\frac{1}{2} m v^2 = \frac{G M m}{R} - \frac{G M m}{2R}$$\frac{1}{2} m v^2 = \frac{G M m}{2R}$$v^2 = \frac{G M}{R}$Since $g = \frac{G M}{R^2}$,we have $G M = g R^2$.Substituting this into the equation for $v^2$:$v^2 = \frac{g R^2}{R} = g R$$v = \sqrt{g R}$

$A$ body which is initially at rest at a height $R$ above the surface of the earth of radius $R$,falls freely towards the earth. Its velocity on reaching the surface of the earth is:

Similar Questions

$A$ body is released from a height equal to the radius $(R)$ of the earth. The velocity of the body when it strikes the surface of the earth will be: (Given $g$ = acceleration due to gravity on the earth.)

Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

$A$ body of mass $m$ is released from a height of $2R$ above the Earth's surface. What will be its kinetic energy at a height of $R$ from the Earth's surface? (Where $R$ is the radius of the Earth)

Under the influence of a central force,which of the following is conserved?

Vedclass Test Series

Exam Paper Generator

Online Exam Module