Question

# An engine increases its angular speed $$300$$ rpm to $$900$$ rpm in $$5$$ seconds. Number of revolutions made during this time by the engine is

A
100
B
75
C
50
D
25

Solution

## The correct option is D $$50$$initial angular velocity, $$\omega_1 = 300 rpm =\dfrac{ 300\times 2\pi}{60} = 10 \pi rad/s$$Final angular velocity, $$\omega_2 = 900 rpm = \dfrac{900\times2\pi }{ 60} = 30\pi rad/s$$Time $$t = 5 s$$(i)Angular acceleration, $$\alpha =\dfrac{\omega_2 -\omega_1}{t}=\dfrac{(30-10)\pi}{5} = \dfrac{20\pi}{5} = 4 pi rad/s^2$$(ii) Angle, $$\theta=\omega_1t+ \dfrac{1}{2}\alpha t^2 = 10pi\times 5 + \dfrac{1}{2}\times4pi \times 25 = 100\pi \quad rad$$Thus, number of revolutions, $$n=\dfrac{100\pi}{2\pi}=50$$  revolutions =Physics

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