Physics, asked by vitamean, 6 months ago

two particles m and 2m are moving along the same line , with speed 2v and v respectively in the same direction, the speed of centre of mass of system is?

Answers

Answered by Mysterioushine
3

Given :

  • Two partcles of masses m and 2m are moving with velocities 2v and v in the same direction along same line

To Find :

  • The speed of the centre of mass of the system

Knowledge Required :

If two masses m₁ and m₂ are moving with speeds v₁ and v₂ in same direction the speed of the centre of mass of the system is given by ,

 \\  \star \: {\boxed{\sf{\purple{V_{COM} = \dfrac{m_1v_1+m_2v_2}{m_1+m_2}}}}}

Solution :

By comparing the data we have with the formulae we get ,

  • m₁ = m , m₂ = 2m
  • v₁ = 2v , v₂ = v

Substituting the values we have in the formulae ,

 \\  :  \implies \sf \: V_{COM} =  \frac{(m)(2v) + (2m)(v)}{m + 2m}  \\  \\

 \\   : \implies \sf \: V_{COM} =  \frac{2mv + 2mv}{3m}  \\  \\

 \\  :  \implies \sf \: V_{COM} =  \frac{4mv}{3m}  \\  \\

 \\  : \implies \sf \: V_{COM} =  \frac{4v}{3}   \\  \\

 \\   : \implies {\underline{\boxed{\pink{\sf{\:V_{COM} = 1.33v}}}}}  \: \bigstar \\  \\

Hence ,

  • The speed of the centre of mass of the systen is 1.33v
Answered by Anonymous
3

\huge\bigstar \:   \huge\mathrm { \underline{ \purple{given} }} \:  \bigstar \:  \\  \\ </p><p>

  • m1 = m

  • m2 = 2m

  • v1 = 2v

  • v2 = v

 \\  \\ \huge\bigstar \:   \huge\mathrm { \underline{ \purple{to \: know} }} \:  \bigstar \: </p><p> \\  \\

\boxed{  \sf{\red{ v_{c.o.m}  =  \frac{m1v1 + m2v2}{m1 + m2} }}}

Putting values ,

 \implies \sf{ \frac{m(2v) + 2m(v)}{m + 2m} } \\  \\   \implies\sf{ \frac{2mv + 2mv}{3m} } \\  \\  \implies \sf{ \frac{4 \cancel{m}v}{3 \cancel{m}} } \\  \\  \sf{ \implies \pink{  \frac{4v}{3} }}

 \therefore \rm{the \: speed \: of \: the \: centre \: of \: mass \: } \\  \rm{ \:  \:  \:  \:  of \: the \: system \: is \:  \blue{ \frac{4v}{3} }} \: .

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