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Question

# As shown in figure, a wheel (r=1 m) is performing combined translational and rotational motion with angular velocity 2 rad/s and the velocity of its centre as −→VO=4^i m/s. Find the velocity of point B in m/s on the wheel.

A
VB=4^i+2^j
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B
VB=2^i4^j
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C
VB=4^i2^j
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D
VB=2^i+4^j
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Solution

## The correct option is C −→VB=4^i−2^jAngular velocity of ring →ω=−2^k rad/s, from right hand thumb rule ⇒Velocity of COM of the ring, −→VO=4^i m/s For the velocity of point B on ring, −→VB=−→VO+→VBO ...(i) Here, →VBO=→ω×→rBO ...(ii) ∵→rBO=1^i, it represents position vector of B w.r.t centre O. ⇒→VBO=(−2^k)×(1^i) →VBO=−2(^k×^i)=−2^j m/s Substituting in Eq (i), −→VB=(4^i−2^j) m/s

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