Question

A wheel is subjected to uniform angular acceleration about its axis. The wheel is starting from rest and it rotates through an angle θ_1, in first two seconds. In the next two seconds, it rotates through an angle θ₂. The ratio θ₁/θ₂ is ____________.

पर्याय

• ${\displaystyle \frac{1}{3}}$

• ${\displaystyle \frac{1}{4}}$

• ${\displaystyle \frac{1}{2}}$

• ${\displaystyle \frac{1}{6}}$

Answer 1

A wheel is subjected to uniform angular acceleration about its axis. The wheel is starting from rest and it rotates through an angle θ_1, in first two seconds. In the next two seconds, it rotates through an angle θ₂. The ratio θ₁/θ₂ is  ${\displaystyle \frac{1}{3}}$.

Explanation:

ln the first 2s the angular displacement of the body

= ${\displaystyle \theta ={\omega }_{0}t+\frac{1}{2} \alpha t^2}$

⇒ ${\displaystyle {\theta }_1=0+\frac{1}{2}\alpha \times 4=2\alpha }$

After a time interval of 4s, the angular displacement of the body = ${\displaystyle \theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2}$

⇒ ${\displaystyle \theta =0+\frac{1}{2}\alpha \times 16=8\alpha }$

To find, the angular displacement in the next 2s, i.e. ${\displaystyle {\theta }_2=\theta -{\theta }_1=6\alpha }$

Ratio ${\displaystyle \frac{{\theta }_1}{{\theta }_2}=\frac{2\alpha }{6\alpha }=\frac{1}{3}}$