A sphere of mass m and radius r rolls without slipping over a tunnel of width `d=(8r)/(5)` as shown in the figure. (in the figure the sphere rolls perpendicular to the plane of the page) the velocity of centre of mass of sphere is v directed into the plane of the page. the maximum speed of a point on the sphere is

Options

A. `(4v)/(3)`
B. `(8v)/(3)`
C. `(6v)/(3)`
D. `(3v)/(2)`

Answer

B

Explanation

`v=omegaxx(3r)/(5)impliesomega=(5v)/(3r)`
`v_(B)=omegaxx(8r)/(5)=(5v)/(3r)xx(8r)/(5)=(8v)/(3)`