A particle A moves along a circle of radius R=10cm so that its radius vector →r relative to O rotates with constant angular velocity ω=0.2rad/s. Find the magnitude of the velocity of the particle and its total acceleration.
A
4cm/s,1.6cm/s2
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B
4cm/s,2.6cm/s2
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C
12cm/s,1.6cm/s2
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D
12cm/s,1.8cm/s2
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Solution
The correct option is A4cm/s,1.6cm/s2
Given that ω0=0.2rad/s,R=10cm=0.1m θc=2θo (from property of circle) ⇒ωc=2ωo=0.4rad/s
(i) Magnitude of velocity |→v|=ωc×R=(0.4)(0.1) ⇒|→v|=0.04m/s or 4cm/s
(ii) Magnitude of total acceleration |→a|=ω2c×R (for uniform circular motion) ⇒|→a|=(0.4)2(0.1)=0.016m/s2 ⇒|→a|=1.6cm/s2