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Which one of the following represents the correct dimensions of the coefficient of viscosity?

  • ML−1 T−2

  • MLT−1

  • ML−1 T−1

  • ML−1 T−1


C.

ML−1 T−1

straight eta space equals space fraction numerator straight F over denominator straight A left parenthesis increment straight V subscript straight x divided by increment straight z right parenthesis end fraction
therefore space Dimensions space of space straight eta
space equals space fraction numerator Dimensions space of space force over denominator Dimensions space of space area space straight x space Dimensions space of space velocity space gradient end fraction
space equals space fraction numerator left square bracket MLT to the power of negative 2 end exponent right square bracket over denominator left square bracket straight L squared right square bracket left square bracket straight T to the power of negative 1 end exponent right square bracket end fraction space equals space left square bracket ML to the power of negative 1 end exponent straight T to the power of negative 1 end exponent right square bracket
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The physical quantity that does not have the dimensional formula [ML-1T-2] is

  • force

  • pressure

  • stress

  • modulus of elasticity


A.

force

As, force = mass x acceleration

⇒   Force = [M] × [M0L1T-2]

⇒   Force = [M1L1T-2]

So, the force does not have the dimensional formula [ML-1T-2]


The set of physical quantities among the following which are dimensionally different is

  • terminal velocity, drift velocity, critical velocity

  • potential energy, work done, kinetic energy

  • dipole moment, electric flux, electric field

  • distintegration constant, frequency, angular velocity


C.

dipole moment, electric flux, electric field

Dipole moment P = q . d Electric Flux, ϕ = E . ds = ML3 I-1 T-3Electric field, E = k . qr2 = ML I-1 T-3


When the voltage and current in a conductor are measured as (100 ± 4) V and (5 ± 0.2) A, then the percentage of error in the calculation of resistance is

  • 8 %

  • 4 %

  • 20 %

  • 10 %


A.

8 %

Given, V ± V = (100 ± 4) V              I ± l = (5 ± 0.2) A RR = VV + ll = 4100 + 0.25 = 0.08 RR % = 0.08 × 100 = 8 %


A dorce F is applied onto a square plate of side L. If the percentage error in determining L is 2 % and that in F is 4 %, the permissible percentage error in determining the pressure is

  • 2 %

  • 4 %

  • 6 %

  • 8 %


D.

8 %

Side of square plate = L

Percentage error in L = 2 %

Percentage error in F = 4 %

We know that, P = FA = FL2

PP × 100 = FF × 100 + 2 LL × 100                    = 4 + 2 (2) %                    = 8 %


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