Unit And Dimensions Set-2

Practice Important MCQs for Unit And Dimensions — Physics, Class JEE.

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Q1. If $E$ and $H$ represents the intensity of electric field and magnetising field respectively, then the unit of $E/H$ will be:

(A)

Joule

(B)

Newton

(C)

Ohm

(D)

Mho

Q2. A physical quantity $\vec{S}$ is defined as $\vec{S} = (\vec{E} \times \vec{B}) / \mu_0$ , where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies):

(A)

Energy

(B)

Force

(C)

Charge $\times$ Current

(D)

Length $\times$ Time

Q3. The density of a material in SI units is 128 kg m $^{-3}$ . In certain units in which the unit of length is 25 cm and the unit of mass 50 g, the numerical value of density of the material is

(A)

(B)

(C)

640

(D)

410

Q4. The dimensional formula of latent heat is:

(A)

$[M L^2 T^{-2}]$

(B)

$[M L T^{-2}]$

(C)

$[M^0 L^2 T^{-2}]$

(D)

$[M L^2 T^{-1}]$

Q5. If $\epsilon_0$ is the permittivity of free space and $E$ is the electric field, then $\epsilon_0 E^2$ has the dimensions:

(A)

$[M L^{-2} T^{-2} A^2]$

(B)

$[M L^{-1} T^{-2}]$

(C)

$[M^{-1} L^{-3} T^4 A^2]$

(D)

$[M L^2 T^{-2}]$

Q6. Given below are two statements:
Statement (I): Dimensions of specific heat is $[L T^{-2} K^{-1}]$
Statement (II): Dimensions of gas constant is $[M L T^{-1} K^{-1}]$

(A)

Statement (I) is incorrect but statement (II) is correct

(B)

Both statement (I) and statement (II) are incorrect

(C)

Statement (I) is correct but statement (II) is incorrect

(D)

Both statement (I) and statement (II) are correct

Q7. What is the dimensional formula of $a b^{-1}$ in the equation $\left( p + \frac{a}{V^2} \right) (V - b) = RT$ , where letters have their usual meaning.

(A)

$[M L^5 T^{-2}]$

(B)

$[M L T^{-2}]$

(C)

$[M L^5 T^{-3}]$

(D)

$[M L^5 T^{-4}]$

Q8. If $G$ be the gravitational constant and $u$ be the energy density then which of the following quantity has the dimension as that of $\sqrt{u G}$ :

(A)

Pressure gradient per unit mass

(B)

Force per unit mass

(C)

Gravitational potential

(D)

Energy per unit mass

Q9. The dimensional formula of angular impulse is:

(A)

$[M L^2 T^{-1}]$

(B)

$[M L^2 T^{-2}]$

(C)

$[M L T^{-1}]$

(D)

$[M L^{-2} T^{-1}]$

Q10. Given below are two statements:
Statement-I: Planck's constant and angular momentum have same dimensions.
Statement-II: Linear momentum and moment of force have same dimensions.

(A)

Statement-I is true but Statement-II is false

(B)

Both Statement-I and Statement-II are false

(C)

Both Statement-I and Statement-II are true

(D)

Statement-I is false but Statement-II is true

Q11. Applying the principle of homogeneity of dimension, which one is correct? where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

(A)

$T^2 = \frac{4\pi^2 r}{G M^2}$

(B)

$T^2 = \frac{4\pi^2 r^3}{G M}$

(C)

$T^2 = \frac{4\pi^2 r^2}{G M}$

(D)

$T^2 = \frac{4\pi^2 r^2}{G M^2}$

Q12. A force is represented by $F = a x^2 + b t^{1/2}$ where $x$ = distance and $t$ = time. The dimensions of $b^2 / a$ are:

(A)

$[M L^3 T^{-3}]$

(B)

$[M L^2 T^{-2}]$

(C)

$[M L^2 T^{-1}]$

(D)

$[M L^2 T^{-3}]$

Q13. If mass is written as $m = k c^P G^{-1/2} h^{1/2}$ then the value $P$ will be: (Constants have their usual meaning with $k$ dimensionless constant)

(A)

1/2

(B)

1/3

(C)

(D)

-1/3

Q14. The equation of state of a real gas is given by $\left(P + \frac{a}{V^2}\right)(V - b) = RT$ where $P$ , $V$ and $T$ are pressure volume and temperature respectively and $R$ is universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of:

(A)

$PV$

(B)

$P$

(C)

$RT$

(D)

$R$

Q15. The frequency $\nu$ of an oscillating liquid drop may depend upon radius $r$ of the drop, density $\rho$ of liquid and the surface tension $s$ of the liquid as: $\nu = r^a \rho^b s^c$ . The values of $a, b$ and $c$ respectively are

(A)

$\left( -\frac{3}{2}, -\frac{1}{2}, \frac{1}{2} \right)$

(B)

$\left( -\frac{3}{2}, \frac{1}{2}, \frac{1}{2} \right)$

(C)

$\left( \frac{3}{2}, -\frac{1}{2}, \frac{1}{2} \right)$

(D)

$\left( -\frac{3}{2}, -\frac{1}{2}, -\frac{1}{2} \right)$

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