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Units And Measurement

Question
CBSEENPH11020525
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If energy (E), velocity (v) and time (T) are chosen  as the fundamental quantities, the dimensional formula of surface tension will be

  • [Ev-2T-1]

  • [Ev-1T-2]

  • [Ev-2T-2]

  • [E-2v-1T-3]

Solution

C.

[Ev-2T-2]

We space know space that surface space tension space left parenthesis straight S right parenthesis space equals space fraction numerator Force space left square bracket straight F right square bracket over denominator Length space left square bracket straight L right square bracket end fraction so comma space left square bracket straight S right square bracket space equals space fraction numerator MLT to the power of negative 2 end exponent over denominator left square bracket straight L right square bracket end fraction space equals space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket Energy space left parenthesis straight E right parenthesis space equals space force space straight x space displacement rightwards double arrow space left square bracket straight E right square bracket space equals space left square bracket ML squared straight T squared right square bracket velocity space left parenthesis straight v right parenthesis space equals displacement over time left square bracket straight v right square bracket space equals space left square bracket LT to the power of negative 1 end exponent right square bracket straight S proportional to space straight E to the power of straight a straight v to the power of straight b straight T to the power of straight c Where space straight a comma space straight b comma space straight c space are space constants From space the space principle space of space homogeneity left square bracket LHS right square bracket space equals left square bracket RHS right square bracket rightwards double arrow space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket ML squared straight T to the power of negative 2 end exponent right square bracket to the power of straight a space left square bracket LT to the power of negative 1 end exponent right square bracket to the power of straight b left square bracket straight T right square bracket to the power of straight c rightwards double arrow space left square bracket ML to the power of 0 straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket straight M to the power of straight a straight L to the power of 2 straight a plus straight b end exponent space straight T to the power of negative 2 straight a minus straight b plus straight c end exponent right square bracket Equating space the space power space on space both space sides comma space we space get straight a equals space 1 comma space 2 straight a space plus straight b space equals 0 comma space straight b equals negative 2 minus 2 straight a minus straight b plus straight c space equals negative 2 straight c equals space left parenthesis 2 straight a plus straight b right parenthesis minus 2 space equals space 0 minus 2 space equals negative 2 left square bracket straight S right square bracket space equals space left square bracket Ev to the power of negative 2 end exponent straight T squared right square bracket space equals space left square bracket Ev to the power of negative 2 end exponent straight T squared right square bracket

Some More Questions From Units and Measurement Chapter

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

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