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 )

This is part of my set Deepanshu's Mechanics Blasts

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