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14. (AIPMT 2010 Prelims )

The dimension of 1 2 ε 0 E 2 , where ε 0 is permittivity of free space and E is electric field, is

(A) ML2T − 2

(B) ML − 1T − 2

(C) ML2T − 1

(D) MLT − 1

Correct answer is (B)

1 2 ε 0 E 2 = Energy density of an electric field E

Also Energy density = E n e r g y V o l u m e = [ M L 2 T − 2 ] [ L 3 ] = [ M L − 1 T − 2 ]

15. (AIPMT 2008 )

Which two of the following five physical parameters have the same dimensions ?
1.  Energy density
2.  Refractive index
3.  Dielectric constant
4.  Young's modulus
5.  Magnetic field

(A) 1 and 4

(B) 1 and 5

(C) 2 and 4

(D) 3 and 5

Correct answer is (A)

Energy density = [ M L 2 T − 2 ] [ L 3 ] = [ M L − 1 T − 2 ]

Young's Modulus(Y) = F A × l Δ l

⇒ [Y] = [ M L T − 2 ] [ L 3 ] [ L ] [ L ] = [ M L − 1 T − 2 ]

16. (AIPMT 2007 )

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

(A) [ML2T − 2]

(B) [ML2T − 1I − 1]

(C) [ML2T − 3I − 2]

(D) [ML2T − 3I − 1]

Correct answer is (C)

We know,

R = V I

∴ [ R ] = [ V ] [ I ] = [ M L 2 T − 3 I − 1 ] [ I ] = [ M L 2 T − 3 I − 2 ]

17. (AIPMT 2005 )

The ratio of the dimensions of Planck's constant and that of moment of inertia is the dimensions of

(A) time

(B) frequency

(C) angular momentum

(D) velocity

Correct answer is (B)

Plank constant (h) = E λ c = [ M L 2 T − 2 ] [ L ] [ L T − 1 ] = [ML2T-1]

Moment of inertia (I) = mr2 = [ML2]

∴ h I = [ M L 2 T − 1 ] [ M L 2 ] = [T-1] = frequency

18. (AIPMT 2004 )

The dimensions of universal gravitational constant are

(A) [M − 1L3T − 2]

(B) [ML2T − 1]

(C) [M − 2L3T − 2]

(D) [M − 2L2T − 1]

Correct answer is (A)

F = G m 1 m 2 r 2

⇒ G = F × r 2 m 1 m 2

∴ Dimension of G = [ M L T − 2 ] [ L 2 ] [ M ] [ M ] = [ M − 1 L 3 T − 2 ]