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

$A$ stationary object is released from a point $P$ at a distance $3R$ from the centre of the moon,which has radius $R$ and mass $M$. Which of the following gives the speed of the object on hitting the moon?

The change in the gravitational potential energy when a body of mass $m$ is raised to a height $h = nR$ above the surface of the Earth is (where $R$ is the radius of the Earth).

From the pole of the earth,a body of mass $m$ is imparted a velocity $v_0$ directed vertically up. If $M$ is the mass of the earth,$R$ its radius and $g$ is the free-fall acceleration on its surface,then the height $h$ to which the body will ascend is (neglect air resistance).

$A$ rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance,the maximum height attained by the rocket above the surface of the earth is

An object of mass $m$ is raised from the surface of the earth to a height equal to the radius of the earth,that is,taken from a distance $R$ to $2R$ from the centre of the earth. What is the gain in its potential energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module