Dimension of `sqrt((in_(0))/(mu_(0)))` are (A) `[M L^(2) T^(-3) A^(-2)]` (B) `[M^(-1) L^(-2) T^(3) A^(2)]` (C) `[M^(2)L^(2)T^(-3) A^(2)]` (D) `[M^(-1) L^(2) T^(3) A^(2)]`

Using method of dimensions, establish the relation among the given quantities. (a) The potential difference V across a conductor depends on current i flowing in it and resistance of conductor R . (b) The speed of light c can be expressed in terms of free space mu_(0) . The energy U stored in an inductor is function of inductance L and current i flowing through it. (d) The time constant tau to R - C circuit can be expressed in terms of resistance R and capacitance. C . Dimensional formulae: V : ML^(2) T^(-3) A^(-1). R: ML^(2) T^(-3) A^(-2) , in_(0) : M^(-1) L^(-3) T^(4) A^(2), mu_(0) : MLT^(-2) A^(2) , L : ML^(2) T^(-2) A^(-2), C : M^(-1) L^(-2) T^(4) A^(2)

Dimensions of epsilon_(0) are M^(-1)L^(-3)T^(4)A^(2) M^(0)L^(-3)T^(3)A^(3) M^(-1)L^(-3)T^(3)A M^(-1)L^(-3)TA^(2)

[M^1 L^2 T^(-3) A^(-2)] is the ………… formula of …………. .

Given that in (alpha//pbeta )=alphaz//K_(B)theta where p is pressure, z is distance, K_(B) is Boltzmann constant and theta is temperature, the dimension of beta are (useful formula Energy =K_(B)xx temperature) (A) L^(0)M^(0)T^(0) " " (B)L^(1)M^(-1)T^(2) " " (C)L^(2)M^(0)T^(0)" "(D)L^(-1)M^(1)T^(-2)

[M^(1) L^(2) T^(-3) A^(-2)] si the dimensional formula of:

If E and G respectively denote energy and gravitational constant,then (E)/(G) has the dimensions of: (1) [M^(2)][L^(-2)][T^(-1)] (2) [M^(2)][L^(-1)][T^(0)] (3) [M][L^(-1)][T^(0)] (4) [M][L^(0)][T^(0)]

Match the physical quantities with dimehnsions expressed in disarray. (i) Angular momentum (i) [M^(-1) L^3T^(-2)] (ii) Latent heat (ii) [M^1 L^3 T^(-3)A^(-2)] (iii) Specific heat (iii) [M^0 L^2 T^(-2)] (iv) Joule's mechanical equivalent of heat (iv) [M^0L^2 T^(-2)K^(-1)] (v) Resistivity (v) [M^0 L^) T^0] (vi) Gravitational Constant (vi) [M^1 L^2 T^(-1)]

Match the following: {:(," ""Column-I",," ""Column-II"),((a),F = A sin(B t) + (1)/(C ln (Dx)) "For above equation to be dimensionally correct",(p),[A] = [M^(1)L^(1)T^(-1)]","[B] = [M^(0)L^(0)T^(-1)]","[C] = [M^(0)L^(0)T^(-1)]),((b) ,"Pressure" = P + (1)/(2)rhov^(2) + gX ,(q),[A] = [M^(0)L^(1)T^(-1)]"," [B] = [M^(0)L^(0)T^(-1)]","[C] = [M^(0)L^(0)T^(-1)]","),((c),X = At+(v)/(B ln(Cr)),(r),[A] = [M^(1)L^(1)T^(-2)]","[B] = [M^(0)L^(0)T^(-1)]","[C] = [M^(-1)L^(0)T^(1)]),(,,(s),"Dimensionally incorrect""):} (Where F = force, P = pressure, rho = density, t = time, v = velocity, a = acceleration, X = displacement)

Match the physical quantities in column A with their dimensional formula expressed in column B {:(Column A,, ColumnB),((1) "Anguar Momentum",,(a)ML^(2)T^(-2)),((2)"Latent Heat",,(b)ML^(2)T^(-2)A^(-2)),((3)"Torque",,(c)ML^(2)T^(-1)),((4)"Capacitance",,(d)ML^(3)T^(-3)A^(-2)),((5)"Inductance",,(e)M^(-1)L^(-2)T^(4)A^(2)),("(Resistivity",,(f)ML^(2)T^(-2)A^(-1)),((7)"Magnetic",,(g)ML^(-1)T^(-2)),((8)"Magnetic",,(h)L^(2)T^(-2)):}

Name the quantites represented by the dimensional formula [M^1 L^2 T^(-1)] , [M^1 L^2 T^(-2)][M^1 L^(-3) T^0].