A particle of mass m_0 is projected from the | vedclass

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

Question

(D) Let the mass of the projected particle be $m_0$. The distance of the particle from each fixed mass $m$ is $l/2$.The gravitational potential energy

Vedclass · Accepted Answer

$2\sqrt{\frac{2Gm}{l}}$

Vedclass · Answer

(D) Let the mass of the projected particle be $m_0$. The distance of the particle from each fixed mass $m$ is $l/2$.The gravitational potential energy $U$ of the particle $m_0$ at the midpoint is given by:$U = -\frac{Gmm_0}{l/2} - \frac{Gmm_0}{l/2} = -\frac{2Gmm_0}{l} - \frac{2Gmm_0}{l} = -\frac{4Gmm_0}{l}$.For the particle to escape to infinity,its total mechanical energy must be at least zero.$E_{total} = KE + PE = 0$$\frac{1}{2}m_0v^2 + U = 0$$\frac{1}{2}m_0v^2 - \frac{4Gmm_0}{l} = 0$$\frac{1}{2}m_0v^2 = \frac{4Gmm_0}{l}$$v^2 = \frac{8Gm}{l}$$v = \sqrt{\frac{8Gm}{l}} = 2\sqrt{\frac{2Gm}{l}}$.

$A$ particle of mass $m_0$ is projected from the midpoint of the line joining two fixed particles,each of mass $m$. If the separation between the fixed particles is $l$,the minimum velocity of projection of the particle so as to escape is equal to:

Similar Questions

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

$A$ mass of $6 \times 10^{24} \ kg$ is to be compressed into a sphere in such a way that the escape velocity from the sphere is $3 \times 10^8 \ m/s$. What should be the radius of the sphere? (Given: $G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$)

State two factors that determine whether a planet will have an atmosphere or not.

The escape velocity of a body from the Earth is about $11.2 \, km/s$. Assuming the mass and radius of the Earth to be about $81$ and $4$ times the mass and radius of the Moon,respectively,the escape velocity in $km/s$ from the surface of the Moon will be .......

The escape velocity of an object from a planet is $16 \ km/s$. If the escape velocity of the object from another planet having twice the density and three times the radius of the planet is $v \sqrt{2} \ km/s$,then the value of $v$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module