The kinetic energy needed to project a body o | vedclass

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

Question

(C) The total energy of a body at the earth's surface is the sum of its kinetic energy $(K.E.)$ and gravitational potential energy $(U)$.$U = -\frac{G

Vedclass · Accepted Answer

$mgR$

Vedclass · Answer

(C) The total energy of a body at the earth's surface is the sum of its kinetic energy $(K.E.)$ and gravitational potential energy $(U)$.$U = -\frac{GM_E m}{R}$To project the body to infinity,the final total energy must be at least zero.By the law of conservation of energy: $K.E. + U = 0$$K.E. - \frac{GM_E m}{R} = 0$$K.E. = \frac{GM_E m}{R}$Since the acceleration due to gravity at the surface is $g = \frac{GM_E}{R^2}$,we can write $GM_E = gR^2$.Substituting this into the expression for kinetic energy:$K.E. = \frac{(gR^2)m}{R} = mgR$

The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is

Similar Questions

The escape velocity from Earth is $v_{es}$. $A$ body is projected with a velocity of $2v_{es}$. With what constant velocity will it move in the interplanetary space?

The escape speed of an object on the surface of the earth is $V$. If the object is thrown out with speed $4V$ from the surface of the earth,what will be the speed of the object far away from the earth?

The mass of a planet is half that of the Earth and the radius of the planet is one-fourth that of the Earth. If we plan to send an artificial satellite from the planet,the escape velocity will be (escape velocity on Earth $v_e = 11 \ km \ s^{-1}$): (in $km \ s^{-1}$)

"The value of the escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet." Is this statement correct? If not,correct it.

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on

Vedclass Test Series

Exam Paper Generator

Online Exam Module