Units and Measurements

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45^th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25^th division coincides with the main scale line?

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL²M^$-$5G^$-$2 are :

Match List I with List II. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} List I List II A. Torque I. Nms$^{ - 1}$ B. Stress II. J kg$^{ - 1}$ C. Latent Heat III. Nm D. Power IV. Nm$^{ - 2}$ Choose the correct answer from the options given below :

Match List I with List II: .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II A. Torque I. $\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-2}$ B. Energy density II. $\mathrm{kg} \,\mathrm{ms}^{-1}$ C. Pressure gradient III. $\mathrm{kg}\, \mathrm{m}^{-2} \mathrm{~s}^{-2}$ D. Impulse IV. $\mathrm{kg} \,\mathrm{m}^{2} \mathrm{~s}^{-2}$ Choose the correct answer from the options given below:

The dimension of magnetic field in M, L, T and C (coulomb) is given as

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be

Identify the pair whose dimensions are equal

Dimensions of ${1 \over {{\mu _0}{\varepsilon _0}}}$, where symbols have their usual meaning, are

The physical quantities not having same dimensions are

Which one of the following represents the correct dimensions of the coefficient of viscosity?

Out of the following pair, which one does NOT have identical dimensions is

Let [${\varepsilon _0}$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:

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 :

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length ?

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:

A quantity f is given by $f = \sqrt {{{h{c^5}} \over G}}$ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :

The dimension of ${{{B^2}} \over {2{\mu _0}}}$, where B is magnetic field and ${{\mu _0}}$ is the magnetic permeability of vacuum, is :