A body is released from a height equal to the | vedclass

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

Question

(A) By the principle of conservation of mechanical energy,the total energy at the initial position (height $h = R$ from the surface,distance $r = 2R$

Vedclass · Accepted Answer

$\sqrt{g R}$

Vedclass · Answer

(A) By the principle of conservation of mechanical energy,the total energy at the initial position (height $h = R$ from the surface,distance $r = 2R$ from the center) is equal to the total energy at the surface of the earth (distance $r = R$ from the center).$U_i + K_i = U_f + K_f$$-\frac{GMm}{2R} + 0 = -\frac{GMm}{R} + \frac{1}{2}mv^2$$\frac{1}{2}mv^2 = \frac{GMm}{R} - \frac{GMm}{2R}$$\frac{1}{2}mv^2 = \frac{GMm}{2R}$$v^2 = \frac{GM}{R}$Since $g = \frac{GM}{R^2}$,we have $GM = gR^2$.Substituting this into the equation for $v^2$:$v^2 = \frac{gR^2}{R} = gR$$v = \sqrt{gR}$

$A$ 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.)

Similar Questions

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?

$A$ body of mass $m$ falls from a height $R$ above the surface of the earth,where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)

$A$ body of mass $m$ is taken from the earth's surface to a height equal to twice the radius $(R)$ of the earth. The change in potential energy of the body will be

An object is propelled vertically to a maximum height of $4 R$ from the surface of a planet of radius $R$ and mass $M$. The speed of the object when it returns to the surface of the planet is

$A$ 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

Vedclass Test Series

Exam Paper Generator

Online Exam Module