2024 Re-NEET System of Particles and Rotational MotionUniform angular velocity Medium Question 12 of 100 in System of Particles and Rotational Motion

Let $\omega_1,\omega_2$ and $\omega_3$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_1,x_2$ and $x_3$ are their respective angular distances in 1 minute then the factor which remains constant (k) is

A $\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}=k$
B $\omega_1x_1=\omega_2x_2=\omega_3x_3=k$
C $\omega_1x_1^2=\omega_2x_2^2=\omega_3x_3^2=k$
D $\omega_1^2x_1=\omega_2^2x_2=\omega_3^2x_3=k$

The answer is A.

Solution

Each hand moves with constant angular speed, so the angular distance covered in 1 minute is $x=\omega\times t$ where $t=60$ s is the same for all hands. Hence $\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}=\dfrac{1}{t}=k$.

Concept Uniform angular velocity

System of Particles and Rotational Motion in past papers

100 questions from this chapter have appeared across 27 exam years.