A particle of mass m is released from infinit | vedclass

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

Question

(C) The total mechanical energy of the particle is conserved. At infinity,the potential energy is $U_{\infty} = 0$ and the kinetic energy is $K_{\inft

Vedclass · Accepted Answer

$\sqrt {\frac{{3GM}}{R}} $

Vedclass · Answer

(C) The total mechanical energy of the particle is conserved. At infinity,the potential energy is $U_{\infty} = 0$ and the kinetic energy is $K_{\infty} = 0$. At the centre of the sphere,the potential energy $U_{c}$ is given by the formula for the potential inside a uniform solid sphere: $U_{c} = m 	imes V_{c} = m 	imes \left( -\frac{3GM}{2R} ight) = -\frac{3GMm}{2R}$. Applying the law of conservation of energy: $K_{\infty} + U_{\infty} = K_{c} + U_{c}$. $0 + 0 = \frac{1}{2}mV^{2} - \frac{3GMm}{2R}$. $\frac{1}{2}mV^{2} = \frac{3GMm}{2R}$. $V^{2} = \frac{3GM}{R}$. $V = \sqrt{\frac{3GM}{R}}$.

$A$ particle of mass $m$ is released from infinity and it moves towards a large solid sphere of mass $M$ and radius $R$ made of a jelly-like material. Neglecting the resistance offered by the material of the sphere,find the velocity of the particle when it crosses the centre of the sphere.

Similar Questions

The gravitational potential energy of a system of three masses $m$,$2m$,and $3m$ placed at the three vertices of an equilateral triangle of side '$a$' is:

Three masses $200 \ kg$,$300 \ kg$,and $400 \ kg$ are placed at the vertices of an equilateral triangle with sides $20 \ m$. They are rearranged on the vertices of a bigger triangle of side $25 \ m$ with the same center. The work done in this process is . . . . . . $J$.

What is gravitational potential energy? What is zero potential energy?

$A$ uniform solid sphere of mass $M$ and radius $R$ is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius $2R$. The value of gravitational potential at a distance $\frac{3}{2}R$ from the center is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module