Angular speed is \(\frac{\pi}{15}\) radians per second. How much time is required to turn through \(240^\circ\)?
Answer and explanation
Correct answer: 20 seconds
Convert \(240^\circ\) into radians: \(240^\circ=\frac{240\pi}{180}=\frac{4\pi}{3}\) radians. Use \(t=\frac{\text{angular displacement}}{\text{angular speed}}\). Thus, \(t=\frac{4\pi/3}{\pi/15}=\frac{4\pi}{3}\times\frac{15}{\pi}=20\) seconds. Therefore, option C is correct. Getting \(24\) seconds indicates an incorrect degree-to-radian conversion. Exam tip: When angular speed is in radians per second, convert the angle to radians first.
Frequently asked questions
What is the correct answer to this question?
20 seconds
Why is this the correct answer?
Convert \(240^\circ\) into radians: \(240^\circ=\frac{240\pi}{180}=\frac{4\pi}{3}\) radians. Use \(t=\frac{\text{angular displacement}}{\text{angular speed}}\). Thus, \(t=\frac{4\pi/3}{\pi/15}=\frac{4\pi}{3}\times\frac{15}{\pi}=20\) seconds. Therefore, option C is correct. Getting \(24\) seconds indicates an incorrect degree-to-radian conversion. Exam tip: When angular speed is in radians per second, convert the angle to radians first.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
