Question

a sphere of mass 50 kilogram and diameter 2m roll without slipping with speed 5 metre per second calculate Total energy​

Answer 1

The ball runs at the speed of 500km per sec

Answer 2

The total kinetic energy of the sphere is 875 reg.

• The total energy of the particle in motion without slipping is the total kinetic energy of the body.
• Total kinetic energy of a body is given by

KE = $\frac{1}{2}mv^2(1+\frac{k^2}{r^2})$

where m is the mass of the body , v is the velocity of the body , r is the radius of the body and k is the radius of gyration of the body.

• The radius of gyration of a solid sphere about the diameter is $\sqrt{\frac{2}{5}}R$.

• Now, substituting the known values , we obtain the total kinetic energy of the body.

m = 50 kilogram

r = 1 m

v = 5 m/s

k = $\sqrt{\frac{2}{5}}R$

• The total KE will be

KE = $\frac{1}{2}50(5)^2(1+\frac{2}{5})$

KE = $25(5)^2(\frac{7}{5})$

KE = 875 erg.

• The total energy of the body is 875 erg.