The masses and radii of the earth and moon ar | vedclass

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

Question

(B) To escape the gravitational influence of both masses,the particle must reach a point where the total gravitational potential energy is zero,which

Vedclass · Accepted Answer

$V = \sqrt{\frac{4G(M_1 + M_2)}{r}}$

Vedclass · Answer

(B) To escape the gravitational influence of both masses,the particle must reach a point where the total gravitational potential energy is zero,which is at infinity. By the law of conservation of energy,the total energy at the midpoint must be equal to the total energy at infinity (which is $0$).At the midpoint,the distance from each mass is $r/2$.The total energy at the midpoint is the sum of kinetic energy and gravitational potential energy:$E_i = \frac{1}{2}mV^2 - \frac{GM_1m}{r/2} - \frac{GM_2m}{r/2}$Setting the total energy to zero:$\frac{1}{2}mV^2 - \frac{2GM_1m}{r} - \frac{2GM_2m}{r} = 0$$\frac{1}{2}mV^2 = \frac{2Gm}{r}(M_1 + M_2)$$V^2 = \frac{4G(M_1 + M_2)}{r}$$V = \sqrt{\frac{4G(M_1 + M_2)}{r}}$

The masses and radii of the earth and moon are $(M_1, R_1)$ and $(M_2, R_2)$ respectively. Their centers are at a distance $r$ apart. Find the minimum escape velocity for a particle of mass $m$ to be projected from the midpoint between these two masses.

Similar Questions

Does the escape speed of a body from the Earth depend on:
$(a)$ the mass of the body,
$(b)$ the location from where it is projected,
$(c)$ the direction of projection,
$(d)$ the height of the location from where the body is launched?

$A$ planet having mass $9 M_e$ and radius $4 R_e$,where $M_e$ and $R_e$ are the mass and radius of the Earth respectively,has an escape velocity in $km/s$ given by: (Given escape velocity on Earth $V_e = 11.2 \times 10^3 \, m/s$)

$A$ body is projected vertically from the Earth's surface of radius $R$ with a velocity equal to half the escape velocity. The maximum height reached by the body is

If the radius and acceleration due to gravity both are doubled,the escape velocity of the Earth will become ......... $km/s$.

The acceleration due to gravity on a planet is the same as that on Earth,and its radius is four times that of Earth. What will be the value of the escape velocity on that planet if it is $v_e$ on Earth?

Vedclass Test Series

Exam Paper Generator

Online Exam Module