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)`
Rightarrow`mgh=1/2J(V/r)^(2)+1/2mv^(2)`
`:.mgh=1/2[1/r^(2)+m]v^(2)`
`:.v^(2)=(mg)/((1/2)[1/r^(2)+m]^(h))`
Rightarrow `valphasqrt(h)`
`:.V_(A)alpha sqrt(h)` and `V_(B)alpha sqrt(4h) Rightarrow V_(B)=2V_(A)`
Also `V_(A)^(2)=2a_(A)h/(sin theta) Rightarrow a_(A)=(gsin thetha)/(1+1/(mr^(2)))`
:.Acceleration of wheel is independent of h
`:.a_(A)=a_(B)`
Also `h/(sin theta)=1/2a_(A)t_(A)^(2) Rightarrow t_(A)alphasqrt(h)`
`:.t_(B)=sqrt((4h)/h)=2 t_(A)`