Two particles each of mass M are released from rest when they are at infinite separation. The velocity of any one when their separation becomes r will be

Question

Two particles each of mass M are released from rest when they are at infinite separation. The velocity of any one when their separation becomes r will be <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/f471dfe0144159ae58ab36ee4c23a283-.png" /> (A) √(2GM/r) (B) √(GM/r) (C) √(GM/r) (D) 2√(GM/2r)

Tardigrade Admin · Accepted Answer

Mv1 - Mv2 = 0 â´ v1 = v2 = v When separation becomes r by using energy conservation -(GMM/r) +(1/2)Mv2 +(1/2)Mv2 = 0 Mv2 = (GMM/r) v = √(GM/r)

Q. Two particles each of mass $M$ are released from rest when they are at infinite separation. The velocity of any one when their separation becomes $r$ will be

$\frac{2 GM}{r}$

$\frac{GM}{r}$

$\frac{GM}{r}$

$2 \frac{GM}{2 r}$

$M v_{1} - M v_{2} = 0$
$∴ v_{1} = v_{2} = v$
When separation becomes $r$ by using energy conservation
$- \frac{GMM}{r} + \frac{1}{2} M v^{2} + \frac{1}{2} M v^{2} = 0$
$M v^{2} = \frac{GMM}{r}$
$v = \frac{GM}{r}$

Q. Two particles each of mass M are released from rest when they are at infinite separation. The velocity of any one when their separation becomes r will be

r2GM​​

rGM​​

rGM​​

22rGM​​

Mv1​−Mv2​=0 ∴v1​=v2​=v When separation becomes r by using energy conservation −rGMM​+21​Mv2+21​Mv2=0 Mv2=rGMM​ v=rGM​​

Q. Two particles each of mass $M$ are released from rest when they are at infinite separation. The velocity of any one when their separation becomes $r$ will be

$\frac{2 GM}{r}$

$\frac{GM}{r}$

$\frac{GM}{r}$

$2 \frac{GM}{2 r}$

$M v_{1} - M v_{2} = 0$
$∴ v_{1} = v_{2} = v$
When separation becomes $r$ by using energy conservation
$- \frac{GMM}{r} + \frac{1}{2} M v^{2} + \frac{1}{2} M v^{2} = 0$
$M v^{2} = \frac{GMM}{r}$
$v = \frac{GM}{r}$