What is the ratio of translational K.E. to the total K.E. of a rolling body?

What is the ratio of rotational K.E. to the translational K.E. of a rolling body?

Two flask A and B of equal volumes maintained at temperature 300K and 700K contain equal mass of He(g) and N_(2)(g) respectively. What is the ratio of total translational kinetic energy of gas in flask A to that of flask B ?

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by v^2=(2gh)/(1+k^2//R^2) using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show K = K + 1/2 MV^2 , where k is the total kinetic energy of the system of particles, K is the total kinetic energy of the system when the particle velcoities are taken with respect to the centre of mass and MV^2//2 is the kinetic energy of the translation of the system as a whole (i,e of the centre of mass motion of the system).

At what distance from mean position is K.E equal to P.E?

Draw a graph to show the variation s of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.

A mixture of Ne and Ar kept in a closed vessel at 250 K has a total K.E.=3 kJ. The total mass of Ne and Ar is 30 g. Find mass % of Ne in gaseous mixture at 250 K.

Two flasks A and B have equal volumes. A is maintained at 300 K and B at 600 K. A contains H_(2) gas, B has an equal mass of CO_(2) gas. Find the ratio of total K.E. of gases in flask A to that of B.

Show that sum of P.E. and k.E. of a freely falling body is conserved.