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Question

Three particles are kept at the three vertices of a right angled triangle as shown:


If each particle starts moving towards the next vertex with the same speed v as shown in the figure. Find the velocity of COM at that instant. (Masses of all particles are same)

A
13[(v3v)^i+2v^j]
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B
13[(v3v2)^i+v2^j]
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C
13[2v^i+3v^j]
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D
13[(v3v2)^iv2^j]
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Solution

The correct option is D 13[(v3v2)^iv2^j]
From the figure, velocities of particles are
VA=v^i, VB=vcos30^i+vsin30^j=3v2^i+v2^j
and VC=v^j
Let mass of each particle be m.
Then,
vcom=mava+mbvb+mcvcma+mb+mc
=m(v^i)+m(3v2^i+v2^j)+m(v^j)m+m+m
vcom=13[(v3v2)^i(v2)^j]
vcom=13[(v3v2)^iv2^j]

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