A hollow sphere of mass 2 kg rolls horizontally on a plane surface without slipping with a constant speed of 1 m/s along a straight line. The total energy of the system is

1.67 Joules

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3.67 Joules

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0.167 Joules

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2.67 Joules

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Solution

The correct option is A 1.67 Joules
The total kinetic energy is due to translational + rotational kinetic energies of the sphere
Total kinetic energy = $m v^{2} / 2 + I ω^{2} / 2 = m v^{2} / 2 + (1 / 2) (2 m R^{2} / 3) (v^{2} / R^{2}) = 5 m v^{2} / 6$
Substituting the values of m and v in the expression, gives KE = $5 \times 2 \times 1^{2} / 6 = 5 / 3 = 1.67 J o u l e s$
The correct option is (a)

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