Units & measurements practice · Mixed difficulty

Given $X = {\left( {Gh/{c^3}} \right)^{1/2}}$ , where G,h and c are gravitational constant, Planck’s constant and the velocity of light respectively. Dimensions of X are the same as those of

Dimensional formula for force is

The unit of self-inductance is

What is the dimension of Luminous flux?

The dimensions of torque are

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49 MSD; 20 divisions on main scale in each $\mathrm{cm}$
For mark on paper
$\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26$
For mark on paper seen through slab
$\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41$
For powder particle on the top surface of the glass slab
$\operatorname{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1$
$(\mathrm{MSR}=$ Main Scale Reading, $\mathrm{VC}=$ Vernier Coincidence)
Refractive index of the glass slab is:

In the context of accuracy of measurement and significant figures in expressing results of experiment, which of the following is/are correct
(1) Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy
(2) If one travels 478 km by rail and 397 m by road, the total distance travelled is 478 km

The number of significant figures in all the given numbers 25.12, 2009, 4.156 and $1.217 \times {10^{ - 4}}$ is

Which of the following is/are the units of strength of magnetic field at a point?

The dimensional formula of coefficient of viscosity is $\left( {F = \eta A\frac{{\Delta V}}{{\Delta x}}} \right)$

Dimensional formula for the universal gravitational constant G is

In the relation $p = \frac{\mathrm{\alpha }}{\mathrm{\beta }}\mathrm{\;}{\mathrm{e}^{ - \frac{{\alpha z}}{{k\mathrm{\theta }}}}},\mathrm{\;}p$ , is the pressure, z the distance, k is Boltzmann constant and $\theta$ is the temperature, the dimensional formula of $\beta$ will be

Statement-I: The number of significant figures in $0.001$ is 1 while in $0.100$ it is 3.
Statement-II: Zeros before a non-zero significant digit are not counted while zeros after a non-zero significant digit are counted.

In which of the following systems of units, a Weber is the unit of magnetic flux?

Which of the following physical quantities have the
same dimensions?

Dimensions of permeability are

A student measured the diameter of a wire using a screw gauge with the least count $0.001 \mathrm{~cm}$ and listed the measurements. The measured value should be recorded as

Which of the following is dimensionless?

The density of a material in CGS system is 8 $g/cm^3$. In a system of a unit in which unit of length is 5 cm and unit of mass is 20 g. The density of material is

The value of Planck's constant in SI unit is

Assertion : The error in the measurement of radius of the
sphere is 0.3%.The permissible error in its surface area is
0.6%.
Reason : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$

The quantity having the same units in all systems of units is

The dimensional formula for Boltzmann’s constant is

Universal time is based on

Error in measurement of radius of sphere is 4% then maximum % error in volume is

Dimensional formula for force is

The velocity of a freely falling body changes as ${g^p}{h^q}$ , where g is acceleration due to gravity and h is the height. The values of p and q are

The dimensions of couple are

If the absolute errors in two physical quantities $A$ and $B$ are $a$ and $b$ respectively, then the absolute error in the value of $A-B$ are

Consider a new system of units in which c(speed of light in vacuum), h(Planck’s constant) and G(gravitational constant) are taken as fundamental units. Which of the following would correctly represent mass in this new system?