Units & measurements practice · Mixed difficulty

A length is measured as $2500 \mathrm{~m}$ by a meter scale. Which of the following statement is correct:

What is the SI unit of surface tension?

If velocity (v), time (T) and mass (M) are taken as fundamental quantities, then dimensional formula for gravitational potential would be.

If muscle times speed equals power, what is the ratio of the SI units and the CGS unit of muscle?

If $\mu_0$ and $\varepsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \varepsilon_0}\right)$ is:

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

Which one of the following does not have the same dimensions

Which of the following is not the unit of energy

Error in the measurement of radius of a sphere is 1%. Then
error in the measurement of volume is

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

Dimensional equation cannot be used

Statement-I: If a physical quantity has a unit, it must not be dimensionless.
Statement-II: No physical quantity exists which has dimension but no unit.

The relation $\tan \theta=v^2 / r g$ gives the angle of banking of the cyclist going round the curve. Here $v$ is the speed of the cyclist, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity. Which of the following statements about the relation is true?

A rectangular beam which is supported at its two ends and leaded in the middle with weight w sags by an amount δ such that $\delta = \frac{{w{l^3}}}{{4Y{d^3}}},\;$, where $l,d$ and Y represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

$\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}} \right]$ are dimensions of

Assertion : Avogadro’s number is the number of atoms
in one gram mole.
Reason : Avogadro’s number is a dimensionless constant.

The dimensions of resistivity in terms of M,L,T and Q where Q stands for the dimensions of charge, is

If $\mathrm{e}$ is charge, $\mathrm{V}$ is potential difference, $\mathrm{T}$ is temperature, then units of $\frac{\mathrm{eV}}{\mathrm{T}}$ are same as of

A physical quantity is represented by $X = {\mathrm{M}^\alpha }{\mathrm{L}^b}{\mathrm{T}^{ - c}}.$. If percentage errors in the measurements of M,L and T are $\alpha \% ,\beta \%$ and $\gamma \%$ respectively, then total, percentage error is

A wire has mass $(0.3\, \pm \,0.003)\,gm,$ radius $(0.5 \pm \,0.005)\,cm\,$ and length $(6 \pm \,0.06)\,cm\,$. The maximum percentage error in the measurement of its density is:-

$\left[ {\mathrm{M}{\mathrm{L}^{ - 2}}{\mathrm{T}^{ - 2}}} \right]$ represents dimensional formula of which of the following physical quantities?

The ratio of SI. Unit of the CGS unit of Planck’s constant is

Which of the following quantities has the same dimensions as that of energy

Unit of stress is

Statement I: The order of accuracy of measurement depends on the least count of the measuring instrument.

Statement II: The smaller the least count, the greater is the number of significant figures in the measured value.

We can reduce random errors by

Statement-1 : Angular momentum and Plank constant have same dimensions.
Statement-2 : Moment of force and linear momentum have same dimensions.

A body travels uniformly a distance of $\left( {20 \pm 0.1} \right)\,\,m$ in time $\left( {2.0 \pm 0.02} \right)\,\,s.$ The velocity of the body is

The dimensions of angular impulse is equal to

The dimensions of pressure are: