Units and Measurement

Distance travelled by linear scale of screw gauge during two full rotation of circular scale is 1mm and circular scale has 50 divisions. In an experiment to measure thickness of a plate, six divisions of main scale are clearly visible and 28th division of circular scale coincides with reference line. Moreover when studs touch each other, zero of circular scale lies 4 division below the reference line, thickness of the plate will be:

If mass M, area A' and velocity V are chosen as fundamental units, then the dimension of coefficient of viscosity will be:

The work done by a gas molecule in an isolated system is given by $W=\alpha {\beta }^2{e}^{-\frac{x^2}{\alpha kT}}$ , where x is the displacement, k is the Boltzmann constant and T is the temperature. a and b are constants. Then the dimensions of b will be:

If $Z=\frac{A^2{B}^3}{C^4},$ $\frac{{}^{}{}^{}}{{}^{}}$ then the relative error in Z will be:

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

Consider the following statements (A) and (B) and identify the correct answer.
(A) A zener diode is connected in reverse bias, when used as a voltage regulator.
(B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.

A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:

A metal wire has mass $(0.4\pm 0.002)\mathrm{g}$ $$ , radius $(0.3\pm 0.001)\mathrm{m}\mathrm{m}$ ${}_{}$ and length $(5\pm 0.02)\mathrm{c}\mathrm{m}$ $$ . The maximum possible percentage error in the measurement of density will nearly be :

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are

If E and G respectively denotes energy and gravitational constant, then E/G has the dimensions of: