A particle is sticked to a disc at a distance r2 m from centre. Disc has initial angular velocity of ωo=6^j rad/s and constant angular acceleration of α=−^j rad/s2 as shown in figure. If radius of disc is 1 m, find the speed of particle after t=2 s.
A
4 m/s
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B
3 m/s
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C
6 m/s
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D
2 m/s
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Solution
The correct option is D2 m/s
Given: ωo=6^j rad/s α=−^j rad/s2 r=1 m
Let angular velocity of disc after time t=2 s is ω
Using ω=ωo+αt ω=6^j−^j×2=4^j rad/s
Using property of rigid body, we can say particle is sticked to disc therefore it will perform circular motion about centre of disc sharing same angular velocity as of disc.
∴Vparticle after 2 s is Vparticle=ω×r2=4^j×12^i m/s=−2^k m/s ∴ Speed of particle after 2 s is 2 m/s