Question

If the original rotational K.E. of the sphere is K, Its new value will be_____ 

(A) (K / n²) 

(B) (K / n⁴) 

(C) n²K 

(D) n⁴K

Answer 1

Correct option: (C) n²K

Explanation:

rotational K.E = (1/2)Iω² 

hence (K¹ / K²) = (I¹ / I²)(ω¹ / ω²)² 

Given K₁ = K, ω₁ = ω

also ω₂ = ω ∙ n² 

hence

(K / K₂) = (I₁ / I₂)(1 / n²)² 

∴ (K / K₂) = [{(2/5)MR₁²} / {(2/5)M(R₁ / n)²}] × (1/n²)² 

(K / K₂) = (n² / n⁴) = (1 / n²)

K² = n² ∙ K