1.

Initial angular velocity of a circular disc of mass M is omega_(1). Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

Answer»

`((M+m)/(M))omega_(1)`
`((M+4m)/(M))omega_(1)`
`((M)/(M+4m))omega_(1)`
`((M)/(M+2m))omega_(1)`

Solution :We KNOW `I_(1)omega_(1)=I_(2)omega_(2)" if "tau=0`
Here `I_(1)=(1)/(2)MR^(2)andI_(2)=(1)/(2)(M+2m)R^(2)`
`therefore (1)/(2)MR^(2).omega_(1)=(1)/(2)(M+2m)R^(2).omega_(2)`
or `omega_(2)=((M)/(M+2m))omega_(1)`


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