Question

A small sphere of mass m and radius R slides down the smooth surface of a large hemispherical bowl of radius R. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point A of the bowl will be:

• A. mg(R − r)
• B. \(\frac{7}{10}mg(R - r)\)
• C. \(\frac{2}{7}mg(R - r)\)
• D. \(\frac{7}{10}mg(R - r)\)

Hint:

For rolling motion, the total kinetic energy is the sum of translational and rotational kinetic energies. Use energy conservation to determine the total kinetic energy at the lowest point.