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# Tag Archives: Math

## What do you mean by degrees of freedom?

What do you mean by degrees of freedom?

Hope that your question is from kinetic theory of gases.

“The number of independent ways by which a dynamic system can move without violating any constraint imposed on it, is called degree of freedom. In other words, the degree of freedom can be defined as the minimum number of independent coordinates that can specify the position of the system completely.”

## Six degrees of freedom

Translation:

Moving up and down (heaving);

Moving left and right (swaying);

Moving forward and backward (surging);

Rotation

Tilts forward and backward (pitching);

Swivels left and right (yawing);

Pivots side to side (rolling).

## Questions from Class XI Physics

1. two boats moving parallel to each other and nearby are pulled towards each other. name the scientific theorem involved in the above cases. state and prove the theorem.

2. what are beats?name the basic phenomenon due to which beats are produced.two sources of sound are producing waves of frequency v1 and v2 where ( v1-v2) is small. show mathematically that the beat frequency is (v1-v2).

3. a body is projected with a velocity ‘u’ at angle theta with the horizontal. derive the mathematical equation of the path followed by the body and hence find the expression for the horizontal range. how will the horizontal range change if the angle of projection is changed to (90- theta).

4. using expression for pressure exerted by a gas on the walls of container, deduce Avogadro’s law.

5. a monkey of mass 40kg climbs on a rope which can with stand a maximum tension of 600N. in which of the following cases will the rope break:

a) if the monkey climbs up with an acceleration of 6m/s2
b) if the monkey climbs down with an acceleration of 4m/s2
c) if the monkey climbs up with a uniform speed of 5m/s
( ignore mass of rope. take g= 10 m/s2)

6. what is the need of banking of tracks?

7. the absolute temperature of a gas is increased to four times. what will be the change in its root mean square speed?

8. find the expression for apparent frequency observed by a stationary observer when a sound emitting source is approaching towards the observer.

9. a body weighs 63N on the surface of earth. what is the gravitational force on it due to the earth at a height equal to half the radius of the earth.

10. show that the co- efficient of superficial expansion of a rectangular sheet of the solid is twice its co-efficient of linear expansion.

(Posted by Ritika)

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