Question

An engine requires 5 seconds to go from a speed of 600 r.p.m. to 1200 r.p.m. How many revolutions does it make in this period?

पर्याय

• 7.5 revolutions

• 75 revolutions

• 750 revolutions

• 7500 revolutions

Answer 1

75 revolutions

Explanation:

`"Initial angular speed,"  omega_0 = (600 xx 2pi)/60`

`= 20pi  "rad/s"`

`"Final angular speed," omega = (1200 xx 2pi)/60`

`= 40pi  "rad/s"`

` therefore  "Angular acceleration,"  alpha = (omega - omega_0)/"t" = (20pi)/5 = 4pi`

∴ Revolutions it makes in t = 5 s is

`theta/(2pi) `

`= (omega_0"t"+1/2 alphat^2)/(2pi) `

`= (20pi xx 5+(1//2)4pi xx25)/(2pi)`

`= 50 + 25`

` = 75`