Correct Answer - Option 1 : 87.5 × 10
-6 joule
CONCEPT:
Kinetic energy (K.E):
- The energy possessed by a body by virtue of its motion is called kinetic energy.
- The expression for kinetic energy is
\(KE = \frac{1}{2}m{v^2}\)
Where m = mass of the body and v = velocity of the body
Rotational Kinetic energy (KE):
- The energy, which a body has by virtue of its rotational motion, is called rotational kinetic energy.
- A body rotating about a fixed axis possesses kinetic energy because its constituent particles are in motion, even though the body as a whole remains in place.
- Mathematically rotational kinetic energy can be written as
\(KE = \frac{1}{2}I{\omega ^2}\)
Where I = moment of inertia and ω = angular velocity.
CALCULATION:
Given - m = 50 g = 0.05 kg, v = 5 cm/s = 0.05 m/s
- The moment of inertia of the rolling ball is
\(\Rightarrow I=\frac{2}{5}mR^2\)
- Kinetic energy due to the rotation is
\(\Rightarrow K_2 = \frac{1}{2}I\omega^2\\ \Rightarrow K_2=\frac{1}{2}\times \frac{2}{5}mR^2\times\frac{v^2}{R^2}\\ \Rightarrow K_2=\frac{1}{5}mv^2\)
\(\Rightarrow K=K_1+K_2\\ \Rightarrow K=\frac{1}{2}mv^2+\frac{1}{5}mv^2\\ \Rightarrow K=\frac{7}{10}mv^2\\\Rightarrow K =0.7\times 0.05\times (0.05)^2\\\Rightarrow K =87.5\times 10^{-6} J\)
- Therefore, option 1 is correct.
