A circular disc of mass M and radius R is rotating about its axis with angular speed ω 1 . If another stationary disc having radius R 2 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω 2 . The energy lost in the process is p% of the initial energy. Value of p is ______

Step-by-step solution

I 1 ω 1 + I 2 ω 2 = I 1 + I 2 × ω f MR 2 2 × ω + 0 MR 2 2 + MR 2 8 16 25 ω f = 4 5 ω Final K . E ., K f = 1 2 MR 2 2 + MR 2 8 16 25 ω 2 K f = MR 2 ω 2 5 ; K i = 1 2 MR 2 2 ω 2 = MR 2 ω 2 4 Percentage loss in kinetic energy %   loss = MR 2 ω 2 4 − MR 2 ω 2 5 MR 2 ω 2 4 × 100 = 20 %