(a) $[M^2L^2T^{-2} $
(b) $[M^2LT^{-2}]$
(c) $ [ML^0T^{-2}]$
(d) None of these
[c]
4. Which of the following have the same dimensions?
(a) Stress
(b) Bulk modulus
(c) Thrust
(d) Energy Density
[a and b]
5. If C and R denote the capacitance and resistance, then the dimension of RC is:
(a) $[M^0L^0T ]$
(b) $[ML^0T] $
(c) $[MLT]$
(d) $[M^0L^0T^2]$
[a]
6. Write any two physical quantities which have the dimension of Energy? [Torque, Work]
7. Is it possible to add any two physical quantities? [No]
8. Force on a sphere of radius 'a' moving in the medium with velocity 'v' is given by $F = 6\pi \eta av $. Find the dimension of $ \eta $. [$ML^{-1}T^{-1}$]
9. What is the dimensional formula for Planck's constant? [$ML^2T^{-1}$]
10. In the formula, $X = 3YZ^2$, X and Z have the dimensions of capacitance and magnetic induction respectively. Find the dimension of Y in MKSQ system. [$M^{-3}L^{-2}T^{4}Q^{4}$]
11. The equation of state for a real gas is given by $ (p+\frac{a}{V^2})(v-b) = RT $. Find the dimensions of 'a' and 'b'. [$[ML^5T^{-2}]$, $[L^3]$]
12. Find the dimension of $\frac{1}{2}\epsilon_0 E^2$. [$ML^{-1}T^{-2}$]
13. A quantity X is given by $ \epsilon_0 L\frac{\Delta V}{\Delta t} $ where $\epsilon_0 $ is the permittivity of the free space, L is the length, $\Delta$V is the potential difference and ${\Delta t}$ is a time interval. The dimensional formula for X is the same as that of (a) Resistance (b) Charge (c) Voltage (d) Current. [d]
14. Pressure depends on distance as $ p = \frac{\alpha}{\beta}e^{-\frac{\alpha z}{k \theta}} $, where $\alpha$, $\beta$ are constant, z is the distance, k is Boltzman's constant and $\theta$ is temperature. Find the dimension of $\beta$. [$L^{2}$]
15. Which of the following pair (s) has the same dimension?
(a) Torque and work
(b) Angular momentum and Work
(c) Energy and Young's modulus
(d) Light-year and Wavelength
(e) Reynold number and co-efficient of friction
(f) Curie and Frequency of the light wave
(g) Latent heat and gravitational potential
(h) Planck's constant and torque
[a,d,e,f,g]
16. Let $ [\epsilon_0]$ denote the dimensional formula of permittivity of the vacuum, and $[\mu_0]$ that of permeability of the vacuum. Find their dimensional formula in term of mass M, length L, time T, and electric current I. [$\epsilon_0 = [M^{-1}L^{-3}T^4I^2]$, $\mu_0= [MLT^{-2}I^{-2}]$]
17. Planck's constant h, speed of light c, and gravitational constant G are used to form a unit of length L and a unit of mass M. Then find the correct option (s) is (are):
(a) $M \propto \sqrt{c}$
(b) $M \propto \sqrt{G}$
(c) $L \propto \sqrt{h}$
(d) $L \propto \sqrt{G}$
[a,c,d]
18. In term of potential difference V, electric current I, permittivity $\epsilon_0$, permeability $\mu_0$ and speed of light c, the dimensionally correct equation(s) is(are):
(a) $\mu_0 I^2 = \epsilon_0V^2$
(b) $ \mu_0 I = \epsilon_0V$
(c) $ I = \epsilon_0 cV$
(d) $ \mu_0 c I = \epsilon_0 V$
[a,c]
19. A length-scale (l) depends on the permittivity ($\epsilon $) of a dielectric material. Boltzmann constant ($k_B$), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and charge (q) carried by each of the particles. Which of the following expression(s) for l is/are dimensionally correct?
(a) $l = \sqrt{\frac{nq^2}{\epsilon k_B T}}$
(b) $l = \sqrt{\frac{\epsilon k_B T}{nq^2}} $
(c) $ l = \sqrt{\frac{q^2}{\epsilon n^{2/3}k_B T}}$
(d) $l = \sqrt{\frac{q^2}{\epsilon n^{1/3}k_B T}}$
[b,d]
20. Give the MKS unit of each of the following:
(a) Young's Modulus
(b) Magnetic Induction
(c) Power of lens
[$N/m^2$, Tesla, Dioptre]
21. A gas bubble, from an explosion underwater, oscillate with a period T proportional to $p^ad^bE^c$, where 'P' is the static pressure, 'd' is the density of the water, and 'E' is the total energy of the explosion. Find the values of a, b, and c. [$a = -\frac{5}{6},b=\frac{1}{2},c=\frac{1}{3}$]
22. Write the dimensions of the following in terms of mass, time, length, and charge
(a) Magnetic flux
(b) Rigidity modulus
[$[ML^2T^{-1}Q^{-1}], [ML^{-1}T^{-2}]$]
23. Match the following with their dimensions where Q is for charge:
|
Column I
|
Column II
|
|
(A) Angular
momentum
|
(a) $[ML^2T^{-2}]$
|
|
(B) Latent Heat
|
(b) $[ML^2Q^{-2}]$
|
|
(C) Torque
|
(c) $[ML^2T^{-1}]$
|
|
(D) Capacitance
|
(d) $[ML^3T^{-1}Q^{-2}]$
|
|
(E) Inductance
|
(e) $[M^{-1}L^{-2}T^{2}Q^2]$
|
|
(F) Resistivity
|
(f) $[L^2T^{-2}]$
|
[$(A) \to (c),(B) \to (f) ,(C)\to (a), (D)\to (e), (E)\to (b),(F)\to (d)$]
24. Match column I with column II:
|
Column I
|
Column II
|
|
(A) Capacitance
|
(i)
Ohm-second
|
|
(B) Inductance
|
(ii)
Coulomb2-joule-1
|
|
(C) Magnetic Induction
|
(iii)
Coulomb (volt)-1
|
|
|
(iv)
Newton (amp-metre)-1
|
|
|
(v)
Volt-second (ampere)-1
|
[$(A) \to (ii),(iii), (B)\to (i),(v), (C)\to (iv)$]
