Dimensions of Physical Quantities

The formula `S = ut - 1/3 at^2` where S is the distance travelled, u is the initial velocity, a is the acceleration and t is the time is ______.

Which of the following physical quantities has neither dimensions nor unit?

If force [F], acceleration [A], and time [T] is chosen as the fundamental physical quantities. Find the dimensions of energy.

A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

Which of the following ratios express pressure?

1. Force/Area
2. Energy/Volume
3. Energy/Area
4. Force/ Volume

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

Which of the following is not a dimensionless quantity?