Units & Measurements

In the formula X = 5YZ2
, X and Z have dimensions of capacitance and magnetic field, respectively. What are
the dimensions of Y in SI units?

The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = \({{{P^3}{Q^2}} \over {\sqrt R S}}.\)
The maximum percentage error in the value of A will be :

The relative error in the determination of the surface area of sphere is \(\alpha\). Then the relative error in the determination of its volume is :

In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25\) \(cm.\) There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main sc...

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 th...

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its
mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum
error in determining the den...

A physical quantity P is described by the relation
P = a\(^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}\) b2 c3 d\(-\)4
If the relative errors in the measurement of a, b, c and d respe...

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 following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 \(\times\) 10-2 m
rise of water, h = 1.45 \(\times\) 10-2m
Using g = 9.80 m/s2 and the simplified relation...

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 :

A, B, C and D are four different physical quantities having different
dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

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...

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

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

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the...

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference
applied across it. If the percentage errors in the measurement of the current and the voltage difference
are 3% each, then error in the...

A screw gauge gives the following reading 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 of the circular scale.
The dia...

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 \(\times\) 10–3 are

In an experiment the angles are required to be measured using an instrument, 29 divisions of the
main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the
main scale is half-a degree(=$$0.5^\cir...

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

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recorded as

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The
total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a
zero error of − 0.03 mm while measu...

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

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

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

The physical quantities not having same dimensions are

Identify the pair whose dimensions are equal