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A particle of mass m, moving in a cicula...

A particle of mass m, moving in a cicular path of radius R with a constant speed `v_2` is located at point (2R,0) at time `t=0` and a man starts moving with a velocity `v_1` along the +ve y-axis from origin at time `t=0`. Calculate the linear momentum of the particle w.r.t. the man as a function of time.

Text Solution

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The correct Answer is:
A, B, C
`vecv_2=(-v_2sinomegat hati+v_2cos omegat hatj),vecv_1=v_1hatj`
`vecv_(PM)=vecv_2-vecv_1`
`=-v_2sinomegat hati+(v_2cos omegat-v_1)hatj`
`vecP_(PM)=mvecv_(PM)`
`=-mv_2sinomegat hati+m(v_2cos omegat-v_1) hatj`
where `omega=(v_2)/R`
or `vecP_(PM)=m[(-v_2sin(v_2)/R thati)+(v_2cos (v_2)/rt-v_1)hatj]`
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