devarshi-dt-logo

Question:

A uniform sphere of mass 500g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 m/s. The total kinetic energy of rolling sphere would be?

0.75×10⁻³J

1.4×10⁻⁴J

5.75×10⁻³J

4.9×10⁻⁵J

Solution:

Correct option is A. 1.4×10⁻⁴J
The total kinetic energy of rolling sphere = Kinetic energy of translation + Kinetic energy of rotation
K=1/2mv² + 1/2Iω²
Since the sphere rolls without slipping
v=Rω
2⇒K=1/2mv² + 1/2(2/5mR²)ω²=1/2mv² + 1/5mv²=7/10mv²=7/10 × 0.5 × 0.02²=1.4×10⁻⁴J