Question

If the angular speed of a particle moving in a circular path of radius \(1.2\) m is increased from \(2\ \text{rad s}^{-1}\) to \(4\ \text{rad s}^{-1}\) keeping its radius constant, then its linear speed is increased by

• A. $1.6\ \text{m s}^{-1}$
• B. $2.4\ \text{m s}^{-1}$
• C. $3.6\ \text{m s}^{-1}$
• D. $4.8\ \text{m s}^{-1}$
• E. $6\ \text{m s}^{-1}$

Hint:

For circular motion: - $v = r\omega$ - Change in linear speed depends directly on change in angular speed if radius is constant

Answer 1

The Correct Option is B

Concept: Linear speed in circular motion is given by: \[ v = r\omega \]

Step 1: Find initial linear speed.
\[ v_1 = r\omega_1 = 1.2 \times 2 = 2.4\ \text{m s}^{-1} \]

Step 2: Find final linear speed.
\[ v_2 = r\omega_2 = 1.2 \times 4 = 4.8\ \text{m s}^{-1} \]

Step 3: Find increase in speed.
\[ \Delta v = v_2 - v_1 = 4.8 - 2.4 = 2.4\ \text{m s}^{-1} \]