EASY
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Write the dimensional formula of Nm2C-1.

Important Questions on Units and Measurements

MEDIUM
If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:
MEDIUM
Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:
EASY
In the following I refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:
MEDIUM
Which of the following combinations has the dimension of electrical resistance (ϵ0 is the permittivity of vacuum and μ0 is the permeability of vacuum)?
MEDIUM
If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ0 can be expressed in units of:
HARD
Let us consider a system of units in which mass and angular momentum are dimensionless. If the length has a dimension of L, which of the following statement (s) is/are correct?
MEDIUM
The dimensions of Stefan-Boltzmann constant σ can be written in terms of Planck's constant h, Boltzmann constant kB and the speed of light c as σ=hαkBβ cγ . Here
EASY
Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:
EASY
Planck's constant (h), speed of light in a vacuum ( c ) and Newton's gravitational constant ( G ) are three fundamental constants. Which of the following combinations of these has the dimension of length?
MEDIUM

Stoke's law states that the viscous drag force F experienced by a sphere of radius aa, moving with a speed v through a fluid with coefficient of viscosity η, is given by F=6πηav.

If this fluid is flowing through a cylindrical pipe of radius r, length l and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as, Vt=kPlaηbrc, where k is a dimensionless constant. Correct values of a, b and c are-

EASY
The ratio of the dimensions of Planck’s constant to that of moment of inertia is the dimension of
EASY
Let L, R, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of LRCV in SI units will be:
EASY
A quantity f is given by f=hc5G where c is speed of light, G universal gravitational constant and h is the Planck’s constant. Dimension of f is that of:
MEDIUM
In  SI units, the dimensions of ϵ0μ0 is:
EASY
Given, B is magnetic field induction, and μ0 is the magnetic permeability of vacuum. The dimension of B22μ0 is:
EASY
If momentum(P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
MEDIUM
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be :
HARD
The dimensions of the area A of a black hole can be written in terms of the universal gravitational constant G, its mass M and the speed of light c as A=GαMβc7. Here-
EASY

Let 0 denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

MEDIUM
A length - scale l depends on the permittivity ε of a dielectric material, Boltzmann constant kB , the absolute temperature T, the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles, Which of the following expressions (s) for l is (are) dimensionally correct?