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Dimensional f...

Question

Dimensional formula for volume elasticity is

A

M^{1} L^{- 2} T^{- 2}

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B

M^{1} L^{- 3} T^{- 2}

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C

M^{1} L^{2} T^{- 2}

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D

M^{1} L^{- 1} T^{- 2}

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Solution

The correct option is D $M^{1} L^{- 1} T^{- 2}$
The volume elasticity is defined as:
Volume elasticity= $\frac{F o r c e / A r e a}{V o l u m e s t r a i n}$

Strain is dimensionless, so
$= \frac{F o r c e}{A r e a} = \frac{M L T^{- 2}}{L^{2}} = [M L^{- 1} T^{- 2}]$

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Similar questions

Þ a = 1/2

Now putting a = 1/2 in equation (3)

Þ

Þ b = 3/2

On substituting value a, b and c in equation (1) T = k(d)^1/2 (r)^3/2 (s)^_1/2

Þ

Hence the correct answer is (c).

Level-3

Illustration 1. A spherical body of mass m and radius r is allowed to fall in a medium of viscosity h. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (t). Dimensionally t can be represented by (5 min)

(a) (b)

(c) (d) None of these

Solution.

The dimensional formulae of mass = [M]

The dimensional formulae of radius = [L]

The dimensional formulae of viscosity = M¹L^_1T¹

So lets check the dimensions of each option

The dimension of is therefore option (a) is not correct.

The dimensions of is therefore option (b) is also not correct.

The dimension of is therefore option (c) is also not correct.

Hence the correct answer is (d).

Illustration 2. The damping force for a body moving through a fluid is proportional to velocity. What will be the dimensional formula for the constant of proportionality ? (3 min)

(a) MLT^_1 (b) ML⁰T^_1

Name the physical quantity whose dimensional formula is (M¹L^-1T^-2)

Q. The dimension of the physical quantity

x

in the equation,

F = \frac{x}{ρ}

F

ρ

is density is given by

Q. Solve this :

32. The dimensions of a/b in the relation

P = \frac{a + x}{b},

where P is pressure and x is distance are -

1) [M^{- 1} L^{- 2} T^{1}] 2) [M^{- 1} L^{1} T^{2}] 3) [M^{1} L^{2} T^{- 1}] 4) [M^{1} L^{- 1} T^{- 2}]

M L^{2} T^{- 2}

is the dimensional formula for

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