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A particle of mass 1 kg has velocity vec...

A particle of mass `1 kg` has velocity `vec(v)_(1) = (2t)hat(i)` and another particle of mass `2 kg` has velocity `vec(v)_(2) = (t^(2))hat(j)`
`{:(,"Column I",,"Column II",),((A),"Netforce on centre of mass at 2 s",(p),(20)/(9) unit,),((B),"Velocity of centre of mass at 2 s",(q),sqrt68 " unit",),((C ),"Displacement of centre of mass in 2s",(r ),(sqrt80)/(3) "unit",),(,,(s),"None",):}`

Text Solution

Verified by Experts

The correct Answer is:
A `rightarrow`q, B `rightarrow`r, C `rightarrow`p
`F_(CM) = F_(1) + F_(2) = m_(1)a_(1)+ m_(2)a_(2) = (2hat(i) + 8hat(j))`
`therefore |F_(CM)| = sqrt(4 + 64)`
`rArr |F_(CM)| = sqrt(68) unit`
`v_(CM) = (m_(1)v_(1) + m_(2)v_(2))/(m_(1)+m)(2)`
`(1)(4hat(i) + 2(4hat(j))/3=(4hat(i) + 8hat(j))/3`
`therefore |v_(CM)| = 1/3sqrt(16 + 64) = sqrt(80)/3 unit`
`s_(1) = (int_(0)^(2))v_(1)dt = (4hat(i)`
`s_(2) = (int_(0)^(2))v_(2)dt = (8/3hat(j)`
`Now, `s_(CM) = ((m_(1)s_(1) + m_(2)s_(2))/(m_(1)+ m_92)`
`=((1)(4hat(i) + 2(8/3hat(j))/3 = (4/3hat(i) = 16/9hat(j))`
`therefore |s_(CM)| = sqrt(16/9 + 256/81) = 20/9`
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