Physical World

and represent the physical quantities inductance, capacitance and resistance respectively. The combinations which have the dimensions of frequency are

In the formula and have dimensions of capacitance and magnetic induction respectively. What are the dimensions of in system?

The pairs of physical quantities that have the same dimensions is (are)

Let denote the dimensional formula of the permittivity of the vacuum and that of the permeability of the vacuum. If = mass, = length, = time and = electric current.

In the relation, is pressure, is distance, is Boltzmann constant and is the temperature. The dimensional formula of will be

A cube has a side of length . Calculate its volume.

A student uses a simple pendulum of exactly length to determine , the acceleration due to gravity. He uses a stopwatch with the least count of second for this and records seconds for oscillations. For this observation, which of the following statements is true ?

Using the expression 2d sin one calculates the values of d by measuring the corresponding angles in the range 0 to 90 . The wavelength X is exactly known and the error in is constant for all values of . As increases from 0

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is seconds and he measures the depth of the well to be meters. Take the acceleration due to gravity and the velocity of sound is . Then the fractional error in the measurement, , is closest to

Consider an expanding sphere of instantaneous radius

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation . If the errors in and are and , respectively, then . The series expansion for , to first power in . is . The relative errors in independent variables are always added. So the error in will be . The above derivation makes the assumption that $\Delta powers of these quantities are neglected. In an experiment the initial number of radioactive nuclei is . It is found that nuclei decayed in the first 1.0 s. For , ln up to first power in . The error , in the determination of the decay constant , in , is

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, and [ The relation between and is

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length and . Which of the following statements is (are) true?

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?