Question

If a solid sphere of mass 1 kg and radius 0.1m olls without slipping at a uniform velocity of 1m/s along a astraight line on a horizontal floor, the kinetic energy is

Answer 1

plz do refer to the image

Answer 2

Answer:

The total kinetic energy in the solid sphere is 0.7 J

Explanation:

The mass of the solid sphere is m=1 kg

The radius of the solid sphere is r=0.1 m

The velocity of the center of mass of the solid sphere is v=1 m/s

The moment of inertia of the solid sphere is

$I=\dfrac{2}{5}mr^2$

The angular velocity if the solid sphere is

$\omega =\dfrac{v}{r}$

The kinetic energy of the center of mass of the solid sphere is $\dfrac{1}{2}mv^2$

The rotational kinetic energy is $\dfrac{1}{2}I\omega^2$

The total kinetic energy is

$KE=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2\\KE=\dfrac{1}{2}mv^2+\dfrac{1}{2}\dfrac{2}{5}mr^2.\dfrac{v^2}{r^2}\\KE=\dfrac{1}{2}mv^2+\dfrac{1}{5}mv^2\\KE= mv^2\left( \dfrac{1}{2}+\dfrac{1}{5} \right )\\KE=\dfrac{7}{10}mv^2\\KE=0.7\times 1\times 1\\KE=0.7\ J$