Circular motion - marble in bowl

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SUMMARY

The discussion focuses on the dynamics of a glass marble of mass m moving in a horizontal circle within a smooth hemispherical bowl of radius r. The marble's center of motion is located 1/2r below the bowl's center. The key findings include the identification of the two forces acting on the marble: gravitational force and the normal reaction force from the bowl. The magnitude of the normal reaction and the speed of the marble can be derived using principles of circular motion and force balance.

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Thanuka
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Can anyone please answer this question

1.A glass marble of mass m is moving int a horizontal circle round the inside surface of a smooth hemispherical bowl of radius r. The centre of the circle is at a distance 1/2r below the centre of the bowl. (i) Find the magnitude of the reaction between the marbel and the bowl (ii) and the speed of the marble.
 
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Note down the two forces acting on the marble.
Marble is moving in a horizontal circle without slipping along the bowl.
So identify equal and opposite camponents of the two forces acting on the marble.
Other camponents of the two forces adds up to give the normal reaction.
 

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