Question

A sphere of mass m rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed ν.

Answer 1

Explanation:

ek=1/2×m×v2

=(m×v2)/2

Answer 2

The kinetic energy of the sphere is $7 / 10 \mathrm{mv}^{2}$when the center moves with the speed of v.

Explanation:

• A sphere with mass m is rolling on a plane surface.
• Let’s consider that it’s radius is R and the center of the sphere moves with the speed/velocity v.

The formula to find the total kinetic energy can be written as

$\text {total kinetic energy} =(1 / 2) I \omega 2+(1 / 2) \mathrm{mv}^{2}$ $\text { Total kinetic energy} =1 / 2 \times 2 / 5 \mathrm{mR}^{2} \mathrm{x} \mathrm{v}^{2} / \mathrm{R}^{2}+1 / 2 \mathrm{mv}^{2}$

                                  $=2 / 10 \mathrm{mv}^{2}+1 / 2 \mathrm{mv}^{2}$

                                  $= 7 / 10 \mathrm{mv}^{2}$

Therefore the kinetic energy at an instant when its center moves with speed v is $7 / 10 \mathrm{mv}^{2}$