A body is projected vertically upwards from t | vedclass

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

Question

(B) The minimum kinetic energy required to escape from the gravitational influence of the earth is given by $K_e = \frac{GMm}{R}$.Given that the kinet

Vedclass · Accepted Answer

$R$

Vedclass · Answer

(B) The minimum kinetic energy required to escape from the gravitational influence of the earth is given by $K_e = \frac{GMm}{R}$.Given that the kinetic energy of projection is $K = \frac{1}{2} K_e = \frac{GMm}{2R}$.At the highest point,the velocity of the body becomes zero,so its kinetic energy is zero.By the law of conservation of energy,the loss in kinetic energy equals the gain in potential energy:$K = U_f - U_i$$\frac{GMm}{2R} = \left( -\frac{GMm}{R+h} \right) - \left( -\frac{GMm}{R} \right)$$\frac{GMm}{2R} = \frac{GMm}{R} - \frac{GMm}{R+h}$Dividing both sides by $GMm$:$\frac{1}{2R} = \frac{1}{R} - \frac{1}{R+h}$$\frac{1}{R+h} = \frac{1}{R} - \frac{1}{2R} = \frac{1}{2R}$$R+h = 2R$$h = R$.

$A$ body is projected vertically upwards from the earth's surface. If its kinetic energy of projection is equal to half of its minimum value required to escape from the gravitational influence,then the height up to which it rises is ($R =$ radius of the earth).

Similar Questions

With what velocity should a particle be projected so that its height becomes equal to the radius of the Earth?

If a body is projected vertically from the surface of the earth with a speed of $8000 \,ms^{-1}$, then the maximum height reached by the body is (Radius of the earth $= 6400 \,km$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $km$)

Work done in raising a body of mass $m$ from the surface of the earth to a height $\frac{R}{3}$ is ......... (where,$R$ is radius of earth,$M$ is mass of the earth and $G$ is gravitational constant)

$A$ body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is (where $g$ is acceleration due to gravity at the surface 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