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Q.

If the frequency of the rotating platform is v and the distance of a boy from the centre is r, what is the area swept out per second by the line connecting the boy to the centre ?

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a

2 $π$ r²v

b

$π$ r²v

c

2 $π$ rv

d

$π$ rv

answer is C.

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Detailed Solution

Question Image

$dA = \frac{1}{2} r x l = \frac{1}{2} r^{2} x ϕ$

$\frac{dA}{dt} = \frac{1}{2} r^{2} \frac{dϕ}{dt} = \frac{1}{2} r^{2} x ω$

$= \frac{1}{2} r^{2} x 2 πv = {πr}^{2} v$

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If the frequency of the rotating platform is v and the distance of a boy from the centre is r, what is the area swept out per second by the line connecting the boy to the centre ?