A disc of mass M = 4 kg, radius R = 1 m is attached with two blocks A and B of masses 1 kg and 2 kg respectively on rim and is resting on a horizontal surface as shown in the figure. Find angular frequency of small oscillation of arrangement:

Options

A. `2.2sec^(-1)`
B. `1.42sec^(-1)`
C. `1.62sec^(-1)`
D. `1.82sec^(-1)`

Answer

B

Explanation

`m_(A)gxxR=m_(B)gRsinthetaRightarrowtheta=30^(@)`in equilibrium
Let it rotated by a clockwise & released.
`Rightarrow tau=20[(cosa)/(2)+(sqrt3)/(2)sina]-10cosa.approx10sqrt3a`
` I=(MR^(2))/(2)+MR^(2)+m_(B)(2Rsin15^(@))^(2)+m_(A)(Rsqrt2)^(2)` =`6+8{(1-cos30)/(2)}+2=12-2sqrt3Rightarrow omega=sqrt((C)/(I))=sqrt((10sqrt3)/(12-2sqrt3))Rightarrow omega=sqrt((5sqrt3)/(6-sqrt3))=1.424sec^(-1)`