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Two particles of equal mass have velocit...

Two particles of equal mass have velocities `` and ``. First particle has an acceleration `` while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

A

straight line

B

parabola

C

circle

D

ellipse

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `vecv_(1)=2hatims^(-1), vecv_(2)=2hatjms^(_1)`.
`veca_(1)=(3hati+3hatj)ms^(-2), veca_(2)=0 ms^(-2)`
`therefore vecv_(CM)= (m_(1)vecv_(1)+m_(2)vecv_(2))/(m_(1)+m_(2))=(vecv_(1)+vecv_(2))/(2)= (2hati+2hatj)/(2)` `(therefore m_(1)=m_(2))`
`=(hati+hatj)ms^(-1)`
Similarly,
`veca_(CM) = (veca_(1)+veca_(2))/(2) = (3hati+3hatj+0)/(2) = 3/2(hati+hatj)ms^(-2)`
Since, `vecV_(CM)` is parallel to `veca_(CM)`, the path will be straight line.
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