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##### 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} .

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

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.

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

(b) How many nanoseconds in 1 year?

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} .