# First Year Physics Measurements EXAMPLE 1.6Find the dimensions and hence the SI units of coefficient of viscosity \eta in the relation of Stokes law for the drag force F for a spherical object of radius r moving with velocity

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##### EXAMPLE 1.6Find the dimensions and hence the SI units of coefficient of viscosity \eta in the relation of Stokes law for the drag force F for a spherical object of radius r moving with velocity v given as F=6 \pi \eta rv.

Name several repetitive phenomenon occurring in nature which could serve as reasonable time standard.

What are the dimensions and units of gravitational constant G in the formula?\[F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}\]

Does dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.

EXAMPLE 1.4Check the correctness of the relation v=\sqrt{\frac{F \times l}{m}} where V is the speed of transverse wave on a stretched string of tension \mathrm{F} length l and mass \mathrm{m} .

Show that the famous "Einstein equation" E=m c^{2} is dimensionally consistent.

Why do we find it useful to have two units for the amount of substance the kilogram and the mole?

EXAMPLE 1.5Derive a relation for the time period of a simple pendulum (Fig. 1.2) using dimensionsal analysis. The various possible factors on which the time period T may depend are(i) Length of the pendulum (l) .(ii) Mass of the bob (\mathrm{m}) .(iii) Angle \theta which the thread makes with the vertical.(iv) Acceleration due to gravity (g).

The length and width of a rectangular plate are measured to be 15.3 \mathrm{~cm} and 12.80 \mathrm{~cm} respectively. Find the area of the plate.

The speed V of sound waves through a medium may be assumed to depend on (a) the density \rho of the medium and (b) its modulus of elasticity E which is the ratio of stress to strain. Deduce by the method of dimensions the formula for the speed of sound.

The period of simple pendulum is measured by a stopwatch. What type of errors are possible in the time period?

Show that the expression \mathrm{V}_{\mathrm{f}}=\mathrm{v}_{\mathrm{i}}+ at dimensionally correct where \mathrm{V}_{1} is the velocity at t=0 a is acceleration and V_{f} is the velocity at time t .

The wavelength \lambda of a wave depends on the speed v of the wave and its frequency f .Knowing that [\lambda]=[L][v]=\left[L T^{-1}\right] and [f]=\left[T^{-1}\right] Decide which of the following is correct f=v \lambda or f=v / \lambda

A light year is the distance light travels in one year. How many metres are there in one light year? (Speed of light =3.0 \times 10^{8} \mathrm{~ms}^{-1} )

Give draw backs to use the period of a pendulum as a time standard.

Find the value of g and its uncertainty using T=2 \pi \sqrt{\frac{l}{g}} from the following measurements made during an experiment.Length of simple pendulum l=100 \mathrm{~cm} Time for 20 vibrations =\mathbf{4 0 . 2 \mathrm { s }} Length was measured by a metre scale of accuracy upto 1 \mathrm{~mm} and time by stop watch of accuracy upto 0.1 \mathrm{~s} .

5.32 . Add the following masses given in kg upto appropriate precision. 2.1890.08911.8 and

Suppose we are told that the acceleration of a particle moving in a circle of radius r with uniform speed v is proportional to some power of r say r^{n} and some power of v say \mathbf{v}^{\mathrm{m}} determine the powers of r and v ?

An old saying is that "A chain is only as strong as its weakest link". What analogue statement can you make regarding experimental data used in computation?