Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc `D_(1)` has 2 kg mass and `0.2` m radius and initial angular velocity of `50rads^(-1)` . Disc `D_(2)` has 4kg mass `0.1m` radius and initial angular velocity of `200rads^(-1)`. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in `rad.s^(-1)`) of the system is

Options

A. 60
B. 100
C. 120
D. 40

Answer

B

Explanation

From law of conservation of angular momentum
`omega_(f) = (I_(1) omega_(1) + I_(2) omega_(2))/(I_(1) + I_(2)) = ((M_(1) R_(1)^(2))/(2) xx 50 + (M_(2) R_(2)^(2))/(2) xx 200)/((M_(1)R_(1)^(2))/(2) + (M_(2) R_(2)^(2))/(2))`
`rArr omega_(f)= (2+ 4)/((1)/(25) + (1)/(50)) = (6)/(3) xx 50 = 100` rad/sec