# Hemispherical bowl For "Thirsty Crows"

Consider an Hollow uniform Hemispherical bowl , which is placed on a rough surfaces( each surface has coefficient of friction $$\mu$$ ) .This hemispherical bowl is used for the purpose of drinking source for Birds and Crow etc. For to comfortable drinking This Bowl must be in equilibrium .

For equilibrium this bowl satisfy the relation :

$$\sin { \theta } \quad =\quad \alpha \cfrac { \mu (\mu +\beta ) }{ { \mu }^{ \gamma }\quad +\quad \delta }$$.

Then Find the value of $$\alpha +\beta +\gamma +\delta$$ ?

Details And Assumptions

$$\bullet$$ Take Centre of mass of Hollow hemisphere at $$\cfrac { R }{ 2 }$$ from base diameter. ( If needed )

$$\bullet$$ Assume that bowl is raised to that much angle which is maximum possible ( which means that is at the verge of slipping )

×