Name several repetitive phenomenon occurring in nature which could serve reasonable times standards

- Give the drawback to use the period of a pendulum as time standard.
**Why do we find it useful to have two units f**or the amount of substance kilogram and the mole?- Three students measured the length of a needle with a scale on which minimum division is 1mm and recorded as (i) 0.2145m (ii) 0.21m (iii) 0.214m which record is correct any why?
- An old saying is that “A chain is only as strong as its weakest link”. What analogous statement can you make regarding experimental data used in a computation?
- The period of simple pendulum is measured by a stop watch what type or errors are possible in the time period?
- Does a dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.
- Write the dimensions of (i) Pressure (ii) Density
- The wavelength of a wave depends on the speed
*v*of the wave and its frequency*f*. Knowing that

[] = [], [v] = [T^{-1}] and [f] = [T]^{-1}

Decide which of the followings id correct, f = V or f =

**NUMERICAL PROBLEMS**

- A light year is the distance light travels in one year. How may meters are there one light year: (speed of light = 3.0 x 10
^{8 }ms^{-1}).

(Ans: 9.5 x 10^{15}m)

- a) How many seconds are there in 1 year?

b) How many nanoseconds in 1 year?

c) How many years in 1 second?

[Ans. (a) 3.1536 x 10^{7 }s, (b) 3.1536 x 10^{16} ns (c) 3.1 x 10-^{8} yr]

- the length and width of a rectangular plate are measured to be 15.3 cm and 12.80 cm, respectively. Find the area of the plate.

(Ans: 196cm^{2})

- Add the following masses given in kg up to appropriate precision 2.189, 0.089, 11.8 and 5.32.

(Ans: 194.4 Kg)

- Find the value of ‘g’ and its uncertainty using T= 2 from the following measurements made during an experiment

Length of simple pendulum = 100 cm

Time of r20 vibrations = 40.2 s

Length was measured by a metre scale of accuracy up to 1 mm and time by stop watch of accuracy up to 0.1s.

(Ans: 9.76 0.06 ms^{-2})

- What are the dimensions and units of gravitational constant G in the formula .

(Ans: [], Nm^{2} Kg^{-2})

- Show that the expression is dimensionally correct, where is the velocity at t=0, a is acceleration and is the velocity at time t.
- The speed v of sound waves through a medium may be assumed to depend on (a) the density of the medium and (b) its modules of elasticity E which is the ratio of stress to strain. Deduce by the method of dimensions, the formula for the speed of sound.

- Show that the famous “Einstein equation” E= mc
^{2}is dimensionally consistent.- 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 v^{m}, determine the powers of r and v?

- 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

(Ans: n = -1, m=2)