A sphere is placed rotating with its centre initially at rest in a corner as shown in Figs.(a) and (b). Coefficient of friction between all surfaces and the sphere is `1//3`. Find the ratio of the friction forces `f_(a)//f_(b)` by ground in situations (a) and (b).

Options

A. `1`
B. `9/10`
C. `10/9`
D. none of these

Answer

B

Explanation

In the figure translatiion equilibrium in vertical direction
`muN_(1)+N_(2)=mg`……..i

In horizontal direction
`N_(1)=muN_(2)`…….ii
Solving eqn i and ii `N_(2)=(mg)/(1+mu^(2))`
The required friction is `muN_(2)=f_(a)=3/10 mg`
In the figure the sphere has the tendency to move towards the right.
`N_(1)=0,N_(2)=mg`
`f_(b)=muN_(2)=(mg)/3`
which gives `(f_(a))/(f_(B))=9/10`