Inside a uniformly accelerating thin-walled spherical shell of radius R which is rolling on horizontal surface there is a small body slipping around Angle of friction between body and inner surface of sphere is `23^(@)` which of the following can be the acceleration a of the center of sphere to ensure that the small body stays at `R//2` distance from the surface?

Options

A. `g/sqrt(3)`
B. `(3g)/4`
C. `g tan 23^(@)`
D. `(gsqrt(3))/2`

Answer

B

Explanation

R is resultant of friction and normal reaction
`Rsin 53^(@)=mg`
`Rcos53^(@)=ma`
`Rightarrow g((cos53^(@))/sin53^(@))=a`
`Rightarrow a=gxxcot53^(@)=3g//4`
other possiblity R is resultant of friction and normal reaction
`R sin 7^(@)=ma`
`R cos7^(@)=ma`
`Rightarrow g((cos7^(@))/sin 7^(@)) Rightarrow a=gxxcot7^(@)` (this option is not given)