1.

Two discs of moments of inertia l_(1) and l_(2) and angular speeds omega_(1) and omega_(2) are rotating along collinear axes pass through their centre of mass and perpendicular to their plane. If the two are made to rotate jointly along the same axis, the rotational K.E. of system will be

Answer»

`((l_(1)omega_(1)+l_(2)omega_(2))^(2))/(2(l_(1)+l_(2)))`
`((l_(1)+l_(2))(omega_(1)+omega_(2)))/2`
`((l_(1)+l_(2))(omega_(1)+omega_(2)))/2`
None of these

Solution :By conservation of angular MOMENTUM,
`I_(1)omega_(1)+I_(2)omega_(2)=(I_(1)+I_(2))OMEGA`
Angular VELOCITY of the system `omega=(I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))`
Rotational kinetic energy `=1/2(I_(1)+I_(2))omega^(2)`
`=1/2(I_(1)+I_(2)).((I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2)))^(2)=((I_(1)omega_(1)+I_(2)omega_(2))^(2))/(2(I_(1)+I_(2)))`


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