Two masses m_1 and m_2 are at rest at infinit | vedclass

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

Question

(B) According to the law of conservation of energy,the initial total energy at infinity is $0$. At a separation $d$,the total energy is the sum of kin

Vedclass · Accepted Answer

$\sqrt{\frac{2G(m_1 + m_2)}{d}}$

Vedclass · Answer

(B) According to the law of conservation of energy,the initial total energy at infinity is $0$. At a separation $d$,the total energy is the sum of kinetic energy and potential energy: $K.E. + P.E. = 0$. Using the reduced mass $\mu = \frac{m_1 m_2}{m_1 + m_2}$,the kinetic energy is $\frac{1}{2} \mu v_{rel}^2$. The potential energy is $-\frac{G m_1 m_2}{d}$. Thus,$\frac{1}{2} \left( \frac{m_1 m_2}{m_1 + m_2} \right) v_{rel}^2 - \frac{G m_1 m_2}{d} = 0$. Solving for $v_{rel}$: $\frac{1}{2} \left( \frac{m_1 m_2}{m_1 + m_2} \right) v_{rel}^2 = \frac{G m_1 m_2}{d}$. $v_{rel}^2 = \frac{2G(m_1 + m_2)}{d}$. $v_{rel} = \sqrt{\frac{2G(m_1 + m_2)}{d}}$.

Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

Similar Questions

What is the change in the gravitational potential energy of an object when it moves away from the Earth and when it comes closer to the Earth?

Assuming that the gravitational potential energy of an object at infinity is zero,the change in potential energy (final - initial) of an object of mass $m$,when moved to a height $h$ from the surface of the Earth (of radius $R$),is given by:

$A$ body starts from rest from a distance $R_0$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be ($R=$ radius of earth,$M=$ mass of earth).

$A$ 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

Under the influence of a central force,which of the following is conserved?

Vedclass Test Series

Exam Paper Generator

Online Exam Module