A vehicle has metal wheels with α = 1.2 × 10 – 5 /°C. It runs at speed of 20 m/s at all the times and covers a distance of 200 km in each run. Its radius is 50 cm at 0°C.

Engineering

Physics

Acceleration

Thermal Expansion

Circular Motion in Vertical Plane

Question

A vehicle has metal wheels with α = 1.2 × 10^{– 5} /°C. It runs at speed of 20 m/s at all the times and covers a distance of 200 km in each run. Its radius is 50 cm at 0°C.

The angular velocity at 50°C is approx. 39.98 rad/s

When the temperature increases, the angular velocity of wheels decreases.

At 50°C, it rotates approx by 39.98 × 10⁵ rad to cover 200 km.

When the temperature increases, the angular velocity of wheels increases.

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

v = ωr

$w = \frac{v}{r} = \frac{20}{r}$

$\frac{20}{0.5} (1 + 1.2 \times 10^{- 5} \times 50)$

= 40 (1 – 6 × 10^{– 4})
= (40 – 24 × 10^{– 3}) = 39.976 rad/s.

$ℓ = Rθ \Rightarrow θ = \frac{200 \times 10^{3}}{0.5 (1 + 1.2 \times 10^{- 5} \times 50)} = 4 \times 10^{5} [1 - 6 \times 10^{- 4}]$

= 4 × 10⁵ (0.9994]
= 3.9976 × 10⁵ rad.