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A uniform rod AB of length three times the radius of a hemispherical bowl remains in equilibrium in the bowl as shown. Neglecting friction find the inclination of the rod with the horizontal.

A uniform rod AB of length three times the radius of a
hemispherical bowl remains in equilibrium in the bowl as
shown. Neglecting friction find the inclination of the rod with
the horizontal.

Question Image
Grade:12th pass

1 Answers

Sachin Kumar
10 Points
4 years ago
since there is equilibrium between rid and bowl
 First draw complete circle to the bowl.
Now make the diameter , through lower end , weight force line and one of the normal line at
othe end meet at a point on the circle D (let)
Now 
by geometry rod divides angle made by rod with 
horizontal and angle made by rod with diameter made by lower end  and joining common
point equally.
 
After this we get an equation  
 
2Rcos2@=1.5Rcos@
ie
2cos2@=1.5cos@
After solving this we get 
cos@=0.92
 

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