A mechanism consists of a part which is translated with a velocity u and a rod AB of length L and mass M hinged at A The rod rotates about axis A with angular velocity `omega` the kinetic energy of rod when it is vertical as shown is

Options

A. `1/2Mu^(2)+1/6ML^(2)omega^(2)`
B. `1/2 Mu^(2)+1/6MLomegau`
C. `1/2Mu^(2)+1/6ML^(2)omega^(2)+1/2MLomegau`
D. none of these

Answer

C

Explanation

`K_(system)=k_(cm)+k_(sys//cm)`
`V_(cm)=u+(wL)/2`
`k_(sys)=1/2m(u+(wL)/2)^(2)+1/2 mL^(2)/12xxw^(2)`
`=1/2mu^(2)+1/8mw^(2)L^(2)+1/8muwL+1/2 mL^(2)/12 w^(2)`
`=1/2mu^(2)+1/8muwL+1/6mw^(2)L^(2)`