MHT CET · Physics · Work Power Energy
A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches the end of diameter in 3 second. The angular speed of the body in rad \(/ \mathrm{s}\) is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Let \(r\) be radius,
Circumference \(=2 \pi\),
Half the circle is covered,
\(\therefore \quad\) Distance covered \(=\pi r=15 r\)
...(given, \(\mathrm{r}=15 \mathrm{~cm}\) )
Speed \(=\frac{\text { distance }}{\text { time }}=\frac{15 \pi}{3}=5 \pi\)
Angular speed, \(\theta=\frac{\mathrm{v}}{\mathrm{r}}=\frac{5 \pi}{15}=\frac{\pi}{3} \mathrm{rad} / \mathrm{s}\)
Circumference \(=2 \pi\),
Half the circle is covered,
\(\therefore \quad\) Distance covered \(=\pi r=15 r\)
...(given, \(\mathrm{r}=15 \mathrm{~cm}\) )
Speed \(=\frac{\text { distance }}{\text { time }}=\frac{15 \pi}{3}=5 \pi\)
Angular speed, \(\theta=\frac{\mathrm{v}}{\mathrm{r}}=\frac{5 \pi}{15}=\frac{\pi}{3} \mathrm{rad} / \mathrm{s}\)
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