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First Year Physics Measurements


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Class 9Class 10First YearSecond Year
ThespeedVofsoundwavesthroughamediummaybeassumedtodependon(a)thedensityρofthemediumand(b)itsmodulusofelasticityEwhichistheratioofstresstostrain.Deducebythemethodofdimensionstheformulaforthespeedofsound.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.

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

Nameseveralrepetitivephenomenonoccurringinnaturewhichcouldserveasreasonabletimestandard.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.
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.

EXAMPLE1.6FindthedimensionsandhencetheSIunitsofcoefficientofviscosityηintherelationofStokeslawforthedragforceFforasphericalobjectofradiusrmovingwithvelocityvgivenasF=6πηrv.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?\[F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}\]
What are the dimensions and units of gravitational constant  G  in the formula?\[F=G \frac{\mathbf{m}_{1} \mathbf{m}_{2}}{\mathbf{r}^{2}}\]

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?
(b) How many nanoseconds in 1 year?

(b)Howmanynanosecondsin1year?(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.
Does dimensional analysis give any information on constant of proportionality that may appear in an algebraic expression? Explain.

Doesdimensionalanalysisgiveanyinformationonconstantofproportionalitythatmayappearinanalgebraicexpression?Explain.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} .
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} .

EXAMPLE1.4Checkthecorrectnessoftherelationv=F×lmwhereVisthespeedoftransversewaveonastretchedstringoftensionFlengthlandmassm.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} .

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