Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

Fill in the blanks: The average kinetic energy of a molecule of a gas is equal to …………

What is the average kinetic energy. Of the molecule of any gas at 100^@C ?

A vibration magnetometer consists of two identical bar magnets, placed one over the other, such that they are mutually perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is 4 second. If one of the magnets is taken away, find the period of oscillation of the other in the same field.

On what factors does the average kinetic energy of gas molecules depend : Nature of the gas, temperature, volume?

The potential energy of a simple harmonic oscillator, when the particle is half way to its end pint is

Explain clearly, with examples, the distinction between :- magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For simplicity, consider one-dimensional motion only].

Read each statement below carefully and state with reasons, if it is true or false: the average speed of a particle is either greater than or equal to the magnitude of average velocity of the particle over the same interval of time.

Two bodies with kinetic energy in the ratio of 4:1 are moving with equal linear momentum. The ratio of their masses is

A proton and an alpha particle having the same kinetic energy are allowed to pass through a uniform magnetic field perpendicular to the direction of their motion. Compare the radii of the paths of the proton and alpha particle.

A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body frm the centre of the star and let its linear velocity be v, angular velocity omega , kinetic energy K, gravitational potential energy U, total energy E and angular momentum p. As the radius r of the orbit increases, determine which of the above quantities increase and which one decrease.