Practice question

Given: A 1100 kg car turns on a banked road ( θ = 20°, μ_s = 0.15 ) with radius 55 m . What is the maximum speed without slipping? (Take g = 10 m/s², tan 20° approx 0.364 ) These values define the system as per NCERT data. Formula: Maximum speed: v_{max = sqrtrg μ_s + tanθ/1 - μ_s tanθ. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Numerator: μ_s + tanθ = 0.15 + 0.364 = 0.514 . Denominator: 1 - 0.15 × 0.364 = 1 - 0.0546 = 0.9454 . v_{max² = 55 × 10 × 0.514/0.9454 approx 550 × 0.5436 approx 298.98 . v_{max = sqrt298.98 approx 17.29 m/s . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.