The pair(s) of physical quantities that do not have the same dimensions, is (are) 

If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimension of the radius of gyration is 

X = 3YZ² find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively

In the relation $P=\frac{\alpha }{\beta }{e}^{-\frac{\alpha Z}{k\theta }}$, P is pressure, Z is the distance, k is the Boltzmann constant and θ is the temperature. The dimensional formula of β will be:

The frequency of vibration of string is given by $\nu =\frac{p}{2l}{\left[\frac{F}{m}\right]}^{1/2}$. Here p is number of segments in the string and l is the length. The dimensional formula for m will be

Choose the correct match 

A wire has a mass of 0.3 ± 0.003 g, radius of 0.5 ± 0.005 mm and length of 0.6 ± 0.006 cm. The maximum percentage error in the measurement of its density will be

The base quantity among the following is 

Assertion : ‘Light year’ and ‘Wavelength’ both measure distance.

Reason : Both have dimensions of time.

Assertion : Light year and year, both measure time.

Reason : Because light year is the time that light takes to reach the earth from the sun.

Assertion : Force cannot be added to pressure.

Reason : Because their dimensions are different.

Assertion : Linear mass density has the dimensions of $\left[M^1{L}^{-1}{T}^o\right]$.

Reason : Because density is always mass per unit volume.

Assertion : Rate of flow of a liquid is defined as volume of liquid flowing per second.

Reason : The dimensions of rate of flow are $\left[M^0{L}^1{T}^{-1}\right]$.

Assertion: Units of Rydberg constant R are m^-1

Reason: It follows from Bohr’s formula $\overline{v}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$, where the symbols have their usual meaning.

Assertion : Parallex method cannot be used for measuring distances of stars more than 100 light years away.

Reason : Because parallex angle reduces so much that it cannot be measured accurately.

Assertion : Number of significant figures in 0.005 is one and that in 0.500 is three.

Reason : This is because zeros are not significant.

Assertion: Out of three measurements l = 0.7 m; l = 0.70 m and l = 0.700 m, the last one is most accurate.

Reason: In every measurement, only the last significant digit is not accurately known.

Assertion: Mass, length and time are fundamental physical quantities.

Reason: They are independent of each other.

Assertion : Density is a derived physical quantity.

Reason : Density cannot be derived from the fundamental physical quantities.

Which of the following is not a unit of time?

Assertion: Nowadays a standard metre is defined in terms of the wavelength of light.

Reason: Light has no relation with length.

Assertion: Surface tension and surface energy have the same dimensions.

Reason: Because both have the same S.I. unit

Assertion : In $y=A\sin (\omega t-kx),$ $(\omega t-kx)$ is dimensionless.

Reason : Because dimension of $\omega =\left[M^0{L}^{0}T\right].$

Assertion : Radian is the unit of plane angle.

Reason : One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

Choose any one of the following four responses :

Assertion : A.U. is much bigger than Å.

Reason : A.U. stands for astronomical unit and Å stands from Angstrom.

Choose any one of the following four responses :

Assertion: When we change the unit of measurement of a quantity, its numerical value changes.

Reason: Smaller the unit of measurement smaller is its numerical value.

Choose any one of the following four responses :

Assertion: Dimensional constants are the quantities whose values are constant.

Reason : Dimensional constants are dimensionless.

Choose any one of the following four responses :

Assertion :The time period of a pendulum is given by the formula, $T=2\pi \sqrt{\text{l}/\text{g}}$.

Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.

Assertion :In the relation $f=\frac{1}{2l}\sqrt{\frac{T}{m},}$ where symbols have standard meaning, m represent linear mass density.

Reason : The frequency has the dimensions of inverse of time.

Choose any one of the following four responses :

Assertion: Avogadro number is the number of atoms in one gram mole.

Reason: Avogadro number is a dimensionless constant.