If a solid sphere of mass 5kg and a disc of mass 4kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be . The the value of x is __________
Show answer and solution
Answer: 5
Solution
For a disc of mass M and radius R, moment of inertia about a tangent in its plane (using parallel axis theorem): I_disc = (1/4)MR² + MR² = (5/4)MR²
With M = 4 kg: I_disc = (5/4)(4)R² = 5R²
For a solid sphere of mass m and radius R, moment of inertia about a tangent (parallel axis theorem): I_sphere = (2/5)mR² + mR² = (7/5)mR²
With m = 5 kg: I_sphere = (7/5)(5)R² = 7R²
Ratio = 5R²/7R² = 5/7
So x = 5
With M = 4 kg: I_disc = (5/4)(4)R² = 5R²
For a solid sphere of mass m and radius R, moment of inertia about a tangent (parallel axis theorem): I_sphere = (2/5)mR² + mR² = (7/5)mR²
With m = 5 kg: I_sphere = (7/5)(5)R² = 7R²
Ratio = 5R²/7R² = 5/7
So x = 5
[JEE Main 2023 · 25 Jan · Shift 2]