Question

If the angular displacement in 10 seconds is $ 150^\circ $, find the number of revolutions in 10 seconds.

• A. 75
• B. 100
• C. 150
• D. 50

Hint:

To find the number of revolutions, divide the angular displacement by \( 360^\circ \), and multiply by the time interval.

Answer 1

The Correct Option is D

We are given the angular displacement \( \theta = 150^\circ \) in 10 seconds. To find the number of revolutions, we first convert the angular displacement from degrees to revolutions. One revolution is \( 360^\circ \), so: \[ \text{Number of revolutions} = \frac{150^\circ}{360^\circ} = \frac{5}{12} \] Since this is the displacement for 10 seconds, the number of revolutions in 1 second is \( \frac{5}{12 \times 10} = \frac{1}{24} \) revolutions per second. In 10 seconds, the number of revolutions is: \[ \text{Number of revolutions} = \frac{1}{24} \times 10 = 50 \]
Thus, the number of revolutions in 10 seconds is \( 50 \).