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Question

A particle is rotating in a circle of radius 1 m with constant speed 4 m/s. In time 1 s
Column - I Column - II (Quantity)(Value in SI units)(a)Displacement(p)8sin2(b)Distance(q)4(c)Average velocity(r)2sin2(d)Average acceleration(s)4sin2

A
a - r; b - p; c - q; d - s
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B
a - r; b - q; c - p; d - s
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C
a - r; b - p; c - r; d - s
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D
a - r; b - q; c - r; d - p
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Solution

The correct option is D a - r; b - q; c - r; d - p
(a) → (r); (b) → (q); (c) → (r); (d) → (p)
Given, v=4 m/s,r=1 m
(a) In 1 s,



θ=lr=41=4
Now in ΔOMB
sinθ2=BMBOsin(42)=BMr
BM=rsin2
required displacement
=2BM
=2sin2
(b) In one second distance =v×t
=4×1=4 m
(c) vaverage=2sin21=2sin2
(d) Change in velocity =vfvi=vf+(vi)
=v2+v2+2×v×vcos(π4)
=2v22v2cos4
=2v2(1cos4)=2vsin2
aaverage=change in velocityt=2vsin2t
=2×vsin2=8sin2

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