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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?$F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}$

$(b) How many nanoseconds in 1 year?$

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

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