Units & measurements practice · Mixed difficulty

Given, Force $= \frac{\alpha }{{\mathrm{density} + \mathrm{\;}{\mathrm{\beta }^3}}}$ What are the dimensions of $\mathrm{\alpha },\mathrm{\beta }?$

The physical quantity which does not have the same dimensions as the other three is

In a slide calliper, $n$ divisions of vernier scale coincides with $(n-1)$ divisions of main scale. The least count of the instrument is

Dimensions of strain are

The fundamental unit, which has the same power in the dimensional formulae of surface tension and viscosity is

Assertion: The number of significant figures in 0.100 is 1 .

Reason: The zeros at the end of a number are always meaningless.

Given that the amplitude A of scattered light is :

(i) Directly proportional to the amplitude $\left(A_o\right)$ of incident light.

(ii) Directly proportional to the volume $(V)$ of the scattering particle

(iii) Inversely proportional to the distance (r) from the scattered particle

(iv) Depend upon the wavelength $(\lambda)$ of the scattered light. then:

Which of the following is not a unit of energy

Rounding off the value 324.13821 upto four significant digits is

Dimensional formula for $\frac{h^2 v^2 / m c^2}{1+\frac{h v}{m c^2}}$ is (where $h$ is planck's constant, $v$ is frequency of light, $m$ is mass and $c$ is speed of light).

The physical quantity which has the dimensional formula $\left[ {{\mathrm{M}^1}{\mathrm{T}^{ - 3}}} \right]$ is

Which of the following physical quantities has neither dimensions nor unit?

Statement-I: Positive zero error is added in measurement.
Statement-II: Defect may occurs during manufacturing of measuring instruments.

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 value of resistance of the wire is

Which of the following measurement is most precise?

Assertion: Mass of a body and the velocity, with which it is moving, cannot be multiplied.

Reason: It is because, mass is a scalar and velocity is a vector quantity. In addition to this, the dimensions of mass and velocity are different.

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 45th 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 25th division coincides with the main scale line?

Which of the following pair of quantities do not have the same dimensions :

The liquid drop of density $\rho ,$ radius $r$ and surface tension $\sigma$ oscillates with time period T. Which of the following expression for ${T^2}$ is correct

Assertion: The dimensional formula for product of resistance and conductance is same as for dielectric constant.

Reason: Both have dimensions of time constant.

Age of the universe is about $10^{10} \mathrm{yr}$, whereas the mankind has existed for $10^6 \mathrm{yr}$. For how many seconds would the man have existed, if age of universe were 1 day?

In the expression for Boyle's law, the product '$P V$' has dimensions of

Dimension of R is

The volume of a cube in ${m}^3$ is equal to the surface area of the cube in ${m}^2$. The volume of the cube is

Assertion: One radian is the angle subtended at the centre of circle by an arc equal in length to the radius fo the circle.
Reason: Radian is the unit of distance

If $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field, then $\varepsilon_0 E^2$ has the dimensions:

Assertion: Force can be subtracted from momentum.
Reason : Physical quantities with different nature and dimensions can be subtracted.

The position of a particle at time t is given by the relation $x\left( t \right) = \left( {\frac{{{v_0}}}{\alpha }} \right)\left( {1 - {c^{ - \alpha t}}} \right)$, where ${v_0}$ is a constant and $\alpha > 0$. The diemensions of ${v_0}$ and $\alpha$ are respectively

The expression $\left[ {\mathrm{M}{\mathrm{L}^{ - 1}}{\mathrm{T}^{ - 1}}} \right]$ represents

Statement-I: The equation $y=x+t$ cannot be true where $x, y$ are the distances and $t$ is time
Statement-II: quantities with different dimensions can not be added