A rigid body starting from rest is rotating about a fixed axis with angular acceleration α = a e⁻ᵇᶿ (where a and b are positive constants) and θ is angular displacement. If maximum angular velocity attained by the body is √(na/b), the value of n is ...
Physics · Mixed Chapter
JEE Mains

Question

A rigid body starting from rest is rotating about a fixed axis with angular acceleration α = a e⁻ᵇᶿ (where a and b are positive constants) and θ is angular displacement. If maximum angular velocity attained by the body is √(na/b), the value of n is ...

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Angular acceleration obeys α=ω(dω/dθ)=a e⁻ᵇᶿ. Starting from rest, integrate ω dω = a e⁻ᵇᶿ dθ. Step 2: (1/2)ω²=(a/b)(1−e⁻ᵇᶿ), so ω²=(2a/b)(1−e⁻ᵇᶿ). Step 3: As θ→∞, ωₘₐₓ=√(2a/b). Thus √(na/b)=√(2a/b), and n=2.