A constant power is supplied to a rotating disc. Angular velocity (ω) of disc varies with number of rotations (n) made by the disc as ω ∝ n¹ᐟˣ. Value of x is
Physics · Mixed Chapter
JEE Mains

Question

A constant power is supplied to a rotating disc. Angular velocity (ω) of disc varies with number of rotations (n) made by the disc as ω ∝ n¹ᐟˣ. Value of x is

G1 Physics · Accepted Answer

Step 1: At constant power P, rotational kinetic energy increases as ½Iω²=Pt (starting from rest), so ω∝t¹ᐟ². Step 2: The angular displacement θ=∫ω dt∝t³ᐟ², so number of revolutions n=θ/(2π)∝t³ᐟ². Step 3: Thus t∝n²ᐟ³ and ω∝n¹ᐟ³. Therefore 1/x=1/3 and x=3.