Two particles of masses m1 and m2 initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time t , when they are at a distance r apart, is

Question

Two particles of masses m1 and m2 initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time t , when they are at a distance r apart, is (A) zero (B) ( textG (( textm)1 ( textm)2/( textr)2) ⋅ (1/( textm)1))t (C) ( textG (( textm)1 ( textm)2/( textr)2) ⋅ (1/( textm)2))t (D) ( textG (( textm)1 ( textm)2/( textr)2) ⋅ (1/( textm)1 + ( textm)2))t

Tardigrade Admin · Accepted Answer

As initially both the particles were at rest therefore velocity of centre of mass was zero and there is no external force on the system so speed of centre of mass remains constant i.e. it should be equal to zero.

Q. Two particles of masses $m_{1}$ and $m_{2}$ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time $t$ , when they are at a distance $r$ apart, is

zero

$(G \frac{( m ) _{1} ( m ) _{2}}{( r ) ^{2}} \cdot \frac{1}{( m ) _{1}}) t$

$(G \frac{( m ) _{1} ( m ) _{2}}{( r ) ^{2}} \cdot \frac{1}{( m ) _{2}}) t$

$(G \frac{( m ) _{1} ( m ) _{2}}{( r ) ^{2}} \cdot \frac{1}{( m ) _{1} + ( m ) _{2}}) t$

As initially both the particles were at rest therefore velocity of centre of mass was zero and there is no external force on the system so speed of centre of mass remains constant i.e. it should be equal to zero.

Q. Two particles of masses m1​ and m2​ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time t , when they are at a distance r apart, is

zero

(G(r)2(m)1​(m)2​​⋅(m)1​1​)t

(G(r)2(m)1​(m)2​​⋅(m)2​1​)t

(G(r)2(m)1​(m)2​​⋅(m)1​+(m)2​1​)t

As initially both the particles were at rest therefore velocity of centre of mass was zero and there is no external force on the system so speed of centre of mass remains constant i.e. it should be equal to zero.

Q. Two particles of masses $m_{1}$ and $m_{2}$ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time $t$ , when they are at a distance $r$ apart, is

$(G \frac{( m ) _{1} ( m ) _{2}}{( r ) ^{2}} \cdot \frac{1}{( m ) _{1}}) t$

$(G \frac{( m ) _{1} ( m ) _{2}}{( r ) ^{2}} \cdot \frac{1}{( m ) _{2}}) t$

$(G \frac{( m ) _{1} ( m ) _{2}}{( r ) ^{2}} \cdot \frac{1}{( m ) _{1} + ( m ) _{2}}) t$