A particle falls from infinity to the earth. Its velocity on reaching earth of radius R is:

Question

A particle falls from infinity to the earth. Its velocity on reaching earth of radius R is: (A)  2Rg  (B)  Rg  (C)  √Rg  (D)  √2Rg

Tardigrade Admin · Accepted Answer

At infinity, potential energy of the particle is zero. When it approaches to earth, its potential energy =- mgR. . This difference in potential energy mgR=(1/2)m upsilon 2 So, upsilon =√2Rg

Q. A particle falls from infinity to the earth. Its velocity on reaching earth of radius R is:

$2 R g$

$R g$

$R g$

$2 R g$

At infinity, potential energy of the particle is zero. When it approaches to earth, its potential energy $= - m g R .$ . This difference in potential energy $m g R = \frac{1}{2} m υ^{2}$ So, $υ = 2 R g$

Q. A particle falls from infinity to the earth. Its velocity on reaching earth of radius R is:

2Rg

Rg

Rg​

2Rg​

At infinity, potential energy of the particle is zero. When it approaches to earth, its potential energy =−mgR. . This difference in potential energy mgR=21​mυ2 So, υ=2Rg​

$2 R g$

$R g$

$R g$

$2 R g$

At infinity, potential energy of the particle is zero. When it approaches to earth, its potential energy $= - m g R .$ . This difference in potential energy $m g R = \frac{1}{2} m υ^{2}$ So, $υ = 2 R g$