Find the dimensions of the following quantities-i the surfaces tension S- ii the coefficient of viscosity -Some equations involving these quantities areS - - g r h-2 and F - - A v2 - v1-x2 - x1Where the symbol have their usual meanings- is density g is acceleration r- h and x are lengthF is force- A is area-

(i) S = ρ g r h/2 or [S] = [ρ][g]L^2 = M/L^3. L/T^2. L^2 = MT^ 2 (ii) F = η A v_2 v_1/x_2 x_1 or, MLT^ 2 = [η]L^2 L/T/L = [η]L^2/T or, [η] = ML^ 1T^ 1 ...

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Byju's Answer

Standard XI

Physics

Dimensional Analysis

Find the dime...

Question

Find the dimensions of the following quantities:
(i) the surfaces tension S, (ii) the coefficient of viscosity $η$ .

Some equations involving these quantities are

$S = \frac{ρ g r h}{2}$ and $F = - η A \frac{v_{2} - v_{1}}{x_{2} - x_{1}}$

Where the symbol have their usual meanings.

$ρ$ is density g is acceleration r, h and x are length

F is force, A is area.

$[S] = M T^{- 2}, [η] = M L^{- 1} T^{- 1}$

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$[S] = M T^{- 2}, [η] = M^{- 2} L T$

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$[S] = M T, [η] = M L^{- 1} T^{- 1}$

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none of these

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Solution

The correct option is A
$[S] = M T^{- 2}, [η] = M L^{- 1} T^{- 1}$

(i) $S = \frac{ρ g r h}{2}$

or $[S] = [ρ] [g] L^{2} = \frac{M}{L^{3}} . \frac{L}{T^{2}} . L^{2} = M T^{- 2}$

(ii) $F = - η A \frac{v_{2} - v_{1}}{x_{2} - x_{1}}$

or, $M L T^{- 2} = [η] L^{2} \frac{\frac{L}{T}}{L} = [η] \frac{L^{2}}{T}$

or, $[η] = M L^{- 1} T^{- 1}$

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Similar questions

Find the dimensions of the following quantities:
(i) the surfaces tension S, (ii) the coefficient of viscosity $η$ .

Some equations involving these quantities are

$S = \frac{ρ g r h}{2}$ and $F = - η A \frac{v_{2} - v_{1}}{x_{2} - x_{1}}$

Where the symbol have their usual meanings.

$ρ$ is density g is acceleration r, h and x are length

F is force, A is area.

Find the dimensions of the following quantities:
(i) the surfaces tension S, (ii) the coefficient of viscosity $η$ .

Some equations involving these quantities are

$S = \frac{ρ g r h}{2}$ and $F = - η A \frac{v_{2} - v_{1}}{x_{2} - x_{1}}$

Where the symbol have their usual meanings.

$ρ$ is density g is acceleration r, h and x are length

F is force, A is area.

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Assuming that F is proportional to different powers of these quantities, guess a formula for F using the

method of dimensions. Use F = - $\frac{η A (v_{2} - v_{1})}{x_{2} - x_{1}}$

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Q. Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque

τ

and
(d) moment of interia I.
Some of the equations involving these quantities are

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The symbols have standard meanings.

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The correct option is A [S]=MT−2,[η]=ML−1T−1 (i) S=ρgrh2 or [S]=[ρ][g]L2=ML3.LT2.L2=MT−2 (ii) F=−ηAv2−v1x2−x1 or, MLT−2=[η]L2LTL=[η]L2T or, [η]=ML−1T−1