A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/^{ }s2)^i+ (4.00 m/s2)^j. At that instant and in unit-vector notation, what is the acceleration of the wallet? IIT JEE- 2001

Options:

A . 2 ^i + 4 ^j

B . 4 ^i + 2 ^j

C . 3 ^i + 6 ^j

D . 3 √5 ^i + 3 √5 ^j

Answer: Option C : C dθdt is constant. In other words in uniform circular motion the angular velocity remains constant body doesn't have any tangential acceleration but normal acceleartion. aN=v2Rorω2R ForpurseaN=√(2)2+(4)2=√20;R=2 ⇒√20=ω22 ⇒ω2=√5 ForwalletaN=ω2R Hence ωis same But~R=3 ⇒aN=√5×3 aN=3√5 So the above answer matches with the magnitude of third option in the given answers.

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