Question:
A particle moves along a circular path of radius '\(r\)' with uniform speed '\(v\)'. The angle described by the particle in two seconds in radians is
A particle moves along a circular path of radius '\(r\)' with uniform speed '\(v\)'. The angle described by the particle in two seconds in radians is
Show Hint
Angular speed is linear speed divided by radius. Multiply by the time to get the angle.
Updated On: Nov 12, 2026
- \(vr^{2}\)
- \(v/r\)
- \(2v/r\)
- \(r/2v\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
In uniform circular motion the angular speed is constant and equals the linear speed divided by the radius.
Step 2: Angular Speed
\(\omega=\dfrac{v}{r}\)
Step 3: Calculation
Angle described in time \(t=2\text{ s}\):
\(\theta=\omega t=\dfrac{v}{r}\times2=\dfrac{2v}{r}\)
Step 4: Compare the options
The result \(\dfrac{2v}{r}\) matches the third option.
Final Answer:
The angle described in two seconds is 2v/r radians. \[ \boxed{\text{(C) }\dfrac{2v}{r}} \]
In uniform circular motion the angular speed is constant and equals the linear speed divided by the radius.
Step 2: Angular Speed
\(\omega=\dfrac{v}{r}\)
Step 3: Calculation
Angle described in time \(t=2\text{ s}\):
\(\theta=\omega t=\dfrac{v}{r}\times2=\dfrac{2v}{r}\)
Step 4: Compare the options
The result \(\dfrac{2v}{r}\) matches the third option.
Final Answer:
The angle described in two seconds is 2v/r radians. \[ \boxed{\text{(C) }\dfrac{2v}{r}} \]
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