Introduction to Physics Physics - Introduction to Physics

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

1. Length, mass and velocity.
2. Length, time and velocity.
3. Mass, time and velocity.
4. Length, time and mass.

A unitless quantity:

1. Never has a non-zero dimension.
2. Always has a non-zero dimension.
3. May have a non-zero dimension.
4. Does not exist.

If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?

The surface tension of water is 72 dyne/cm. Convert it in SI unit.

Taking force, length and time to be the fundamental quantities find the dimensions of:

1. Density.
2. Pressure.
3. Momentum.
4. Energy.

Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a metre stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?

If two quantities have same dimensions, do they represent same physical content?

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are not?

Theory of relativity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a relation among the quantities using the method of dimensions.

The frequency of vibration of a string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.