The 50kg homogenous smooth sphere rests on the `30^(@)` incline A and bears against the smooth vertical wall B.Calculate the contact forces at A and B.

Options

A. `N_(A)= 1000/sqrt(3) N, N_(B) = 500/sqrt(3)` N
B. `N_(A) = 1000/sqrt(3) N, N_(B) = 1000/sqrt(3) N`
C. `N_(A) = 500/sqrt(3) N, N_(B) = 500/sqrt(3) N`
D. `N_(A) = 500/sqrt(3) N, N_(B) = 1000/sqrt(3) N`

Answer

A

Explanation

`mg - N_(A) cos 30=0` [Eqluilibrium in vertical direction]
`rArr N_(A) = (mg)/(cos 30^(@))`
`rArr N_(A)= 1000/sqrt(3) N`
`N_(B)- N_(A) sin 30 =0` [Equilibrium in horizontal]
`rArr N_(B) = N_(A) sin 30`
`rArr N_(B) = 1000/sqrt(3) xx 1/2`
`rArr N_(B) = 500/sqrt(3) N`