Block `A` shown in figure can slide over fixed rigid wire of quarter cicular shape in vertical plane String connected to `A` and `B` is massless and inextensible. System is released from rest when `theta = 0`. Determine the ratio `k = (M_(A))/(M_(B))` (approximate integer value) for whoch the system will come to rest again when `theta = 30^(@)`.

Answer

3

Explanation

`M_(B)g(sqrt(2)R - R)-M_(A)g(R- (Rsqrt(3))/(2)) = 0`
`rArr (M_(A))/(M_(B)) = (sqrt(2) - 1)/(1 - (sqrt(3))/(2)) = (0.41)/(1-0.86) = (0.41)/(0.14) = 3`