Question

The velocity and acceleration vectors of a particle undergoing circular motion are \( \vec{v} = 2i + 4j \, \text{m/s} \) and \( \vec{a} = 2i + 4j \, \text{m/s}^2 \) respectively at an instant of time. The radius of the circle is a

• A. 1 m
• B. 2 m
• C. 3 m
• D. 4 m

Hint:

In circular motion, the radius can be determined using the formula \( r = \frac{v^2}{a} \), where \( v \) is the speed and \( a \) is the acceleration.

Answer 1

The Correct Option is A

Step 1: Use the relationship between velocity, acceleration, and radius in circular motion.
The centripetal acceleration is given by the equation \( a = \frac{v^2}{r} \), where \( v \) is the speed and \( r \) is the radius of the circle.
Step 2: Calculate the magnitude of velocity and acceleration.
Magnitude of \( \vec{v} = \sqrt{(2)^2 + (4)^2} = \sqrt{20} = 2\sqrt{5} \, \text{m/s} \)
Magnitude of \( \vec{a} = \sqrt{(2)^2 + (4)^2} = \sqrt{20} = 2\sqrt{5} \, \text{m/s}^2 \)
Step 3: Apply the formula for centripetal acceleration.
\( r = \frac{v^2}{a} = \frac{(2\sqrt{5})^2}{2\sqrt{5}} = 1 \, \text{m} \) Final Answer: \[ \boxed{1 \, \text{m}} \]