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The angular velocity of a wheel increase...

The angular velocity of a wheel increases from 120 to 480 rpm in 10 s .The number of revolutions made during this time is

A

100 rev

B

150 rev

C

200 rev

D

250rev

Text Solution

Verified by Experts

The correct Answer is:
D
`n_(1) = (600) / (60)= 10 r.p.s and n_(2) =(2400)/(60) = 40 r.p.s `
the angular accleration ,
` alpha =(omega _(2) - omega_(1))/(t)= (2pi ( n_(2)-n_(1)))/(t) =(2pi (40-10))/(10)`
` therefore alpha = 6 pi rad//s^(2)`
`therefore ` The angle described in 10 S
` theta = omega_(1) =(1)/(2) alpha t ^(2) = 20 pi pi xx10 +(1)/(2) (6 pi) xx100`
`= 200 pi + 30 pi = 500 pi `
` therefore ` The no. of revolutions `=("Total angle")/(2pi)`
`therefore N=(500 pi)/(2pi) = 250`
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