Portion `AB` of the wedge shown in figure is rough and `BC` is smooth. A solid cylinder rolld without slipping from `A` to `B`. Find the ratio of translational kinetic energy to rotational kinetic energy, when the cylinder reaches point `C`.
.

Options

A. `3//5`
B. `5`
C. `7//5`
D. `8//3`

Answer

B

Explanation

For a cylinder `(K_(T))/(K_(R))=2` in case of pure rolling
Upto `B`
` K_(T)=2/3 mgh` and `K_(R)=1/3mgh`

After `B`: rotational kinetic energy is constant, however, translational kinetic energy increases.
At `C: K_(T)=2/3mgh+mgh=5/3`
While `K_(R)=1/3mgh, (K_(T))/(K_(R))=5`