Two wheels `A` and `B` are released from rest from points `X` and `Y` respectively on an inclined plane as shown in the figure. Which of the following statement(s) is/are incorrect?

Options

A. Wheel `B` takes twice as much time to roll from `Y` to `Z` than that of wheel `A` from `X` to `Z`.
B. At point `Z` velocity of wheel `A` is four times that of wheel `B`.
C. Acceleration of the wheel `A` is twice that of the wheel `B`.
D. Both wheel take same time to arrive at point `Z`

Answer

B, C, D

Explanation

Using law of conservation of energy for wheel `A`
`mgh=1/2Iomega^(2)+1/2mv^(2)`
`mgh=1/2I(V/R)^(2)+1/2mv^(2)`
`v^(2)=(mg)/(1/2[I/r^(2)+m])h`
`vpropsqrth`
`V_(A)propsqrth` and `V_(B)propsqrt(4h)`
`V_(B)=2V_(A)`
Also `v_(A)^(2)=2a_(A) h/(sintheta)impliesa_(A)=(gsintheta)/(1+1/(mr^(2)))`
Acceleration of wheel is independent of h
`aA=aB`
Also `h/(sintheta)=1/2a_(A)+t_(A)^(2)impliest_(A)propsqrth`
`(t_(B))/(t_(A))=sqrt((4h)/h)=2`