A particle rotating in x-y plane on a circle of radius 2 m as shown. At certain instant particle is at point P and its acceleration is 6 i ^ − 8 j ^ . Then at this moment:

Question

A particle rotating in x-y plane on a circle of radius 2 m as shown. At certain instant particle is at point P and its acceleration is 6 i ^ − 8 j ^ ​ . Then at this moment:

TestHub · Accepted Answer

At P (top of circle), centripetal acceleration points to the centre: $a_{c} = - 8 \hat{j}$ , so $\frac{v ^{2}}{r} = 8$ , $v = 4$ m/s. (D) correct

Tangential part $6 \hat{i} = α \times r = (α \hat{k}) \times (2 \hat{j}) = - 2 α \hat{i}$ , giving $α = - 3 \hat{k}$ . (A) correct

$ω = \frac{v}{r} = 2$ ; with $a_{t} = + 6 \hat{i}$ at the top, rotation is clockwise: $ω = - 2 \hat{k}$ . (C) correct

Velocity is $+ 4 \hat{i}$ , not $- 4 \hat{i}$ , so (B) is wrong

Answer: (A), (C), (D)

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