Assignment of UNITS AND DIMENSIONS

                UNITS AND DIMENSIONS

Q1. the correct order in which the dimensions of length increases in the following quantities is :

(i)permittivity  (ii) resistance  (iii) magnetic permeability  (iv)stress

(a)(i),(ii),(iii),(iv)   (b) (iv),(iii),(ii),(i)    (c) (i),(iv),(iii),(ii)       (d) (iii),(ii),(iv),(i)

Q2. the ratio of the dimensions of Plank’s constant and that of moment of inertia is the dimension of :

(a)time    (b)frequency   (c)angular momentum   (d)velocity

Q3. consider the following equation of Bernoulli’s theorem

                   P+ pv² +pgh =K (constant )

The dimension of K/P are :

(a)thrust         (b)pressure    (c)angle   (d)viscosity

Q3. Dimensions of electric resistance is :

(a)[ML²T^-3A^-1]         (b) [ML²T^-3A^-2]    

 (c) [ML³T^-3A^-2]         (d) [ML^-1T³A²]

Q4. In a system of unit, if force (F), acceleration (A) and time (T) are taken as fundamental units then the dimensional formula for energy is :

(a) [FA²T]        (b) [FAT²]      

 (c)[FA²T]         (d)[FAT]

Q5. which of the following is not a unit of young’s modulus ?

(a) Nm^-1           (b) Nm^-2     (c)dyne cm^-2   (d)megapascal

Q6. Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant?

(a)Acceleration due to gravity                   (b)Surface tension of water  

 (c)Weight of a standard kilogram mass   (d)The velocity of light on vacuum

Q7. SI unit of magnetic flux is :

(a)tesla      (b)oersted    (c)weber      (d)gauss

Q8.Which of the following group have different dimension?

(a)Potential difference, emf, voltage       (b)pressure, stress,  Young’s modulu (c)Heat, energy, work done   (d)Dipole moment, electric flux, electric field

Q10. The unit of electric field is not equivalent to :

(a)J/C     (b)J/cm     (c)V/m    (d)N/C

Q11. If E and B respectively represent electric field and magnetic field, then the ratio E/B has the dimension of:

(a) displacement  (b)velocity    (c)acceleration    (d)angle

Q12. The dimension of  E₀E² , where E₀ is permittivity of free space and E electric field, is

(a)[ML2T^-2] (b) )[ML^-1T^-2]  (c) )[ML²T^-1]  (d) )[MLT^-1]

Q13. The mass and volume of a body are found to be 5.00 ±0.05kg and 1.00±0.05m³ respectively. Then the maximum possible percentage error in its density is :

(a)6%      (b)3%     (c)10%      (d)5%      (e)7%

Q14. In an experiment four quantities a,b,c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows:

        P= a³b²/cd

Percentage error in P is

(a)10%      (b)7%       (c)4%     (d)14%

Q15. the dimesion of the quantity E x B, where E  represents the electric field and B the magnetic field may be given as:

(a)[MT^-3]     (b)[M²LT^-5A^-2]                                                                         (c) [M²LT^-3A^-1]     (d) [MLT^-2A^-2]

Q16. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are

(a)[FVT^-1]     (b)[FVT^-2]                                                                                  (c)[FV^-1T^-1]     (d)[FV^-1T]

Q17. the dimensions of mobility of charge carriers are: 

(a) [M^-2T²A] (b) [M^-1T²A]                                                                                (c) [M^-2T³A] (d) [M^-1T³A] (e) [M^-1T²A^-1]

Q18. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formulae of surface tension will be :

(a)[EV^-1T^-2] (b) [EV^-2T^-2]                                                                                   (c) [E²V^-1T^-2] (d) [EV^-2T^-1]

Q19. Plank’s constant (h), speed of light in volume (c) and Newton’s gravitational constant (G) are three fundamental constants. What is the dimension of length

Q20. Which of the following unit denotes the dimension [ML²/Q²]. Where Q denotes the electric charge.

(a)weber (Wb)         (b)Wb/m²      (c)henry (H)        (d)H/m²

Q21. The magnetic moment has dimension of

(a)[LA]         (b)[L²A]          (c) [LT^-1A]           (d)[L²T^-1A]

Q22. Surface tension has the same dimension as of :

(a)Coefficient of viscosity      (b)impulse      (c)momentum   (d)spring constant    (e) frequency

Q23. which of the following sets of quantities have same dimensional formulae?

(a) Frequency, angular frequency and angular momentum    

(b)surface tension, stress and spring constant

 (c)acceleration, momentum and retardation 

 (d)Thermal capacity, specific heat and entropy

 (e) Work, energy and torque

Q24. A physical quantity P=  / d³e^1/3 is determined by measuring a, b, c,d  and separately with the percentage error of 2%, 3%, 2%, 1% and 6% respectively. Minimum amount of error is contributed by the measure of :

(a)b        (b)a      (c)d       (d)e   (e)c

Q25. Two forces 5N and 12N simultaneously  act on a particle. The net force on particle is

(a) 17N     (b) 12N     (c) 13N      (d) 7N

Q26. A physical quantity Y= a⁴b⁴ / (cd⁴)^1/3 has four observables a, b, c, and d. the percentage error in a, b, c and d are 2%, 3%, 4% and 5% respectively. The error in y will be :

(a) 6%    (b)11%     (c)12%     (d)22%

Q27. which of the following quantities measured from different inertial reference frames are same ?

(a)force     (b)velocity   (c)displace  (d)kinetic energy

Q28. If the unit of mass, length and time are doubled, unit of angular momentum will be :

(a)doubled   (b)tripled    (c)quadrupled  (d) 8 times the original value

Q29. If E= energy , G gravitational constant,  I = impulse and M = mass, the dimension of GIM²/E² are same that of

(a)time   (b)mass      (c)length  (d)force

Q30. A new system of unit is evolved in which the values of µ0 and E0 are 2 and 8 respectively. Then the speed of light in this system will be

(a)0.25         (b) 0.5      (c)0.75     (d)1.0

Q31.The velocity of a particle (v) at an instant t is given by ; v=at+bt² the dimension of b is :

(a)[L]                          (b) [LT^-1]

(c)[LT^-2]                      (d)[LT^-3]

Q32. If the dimensions of a physical quantity are given by M^aL^bT^c,then the physical quantity will be :

(a)velocity if a=1,b=0,c=-1

(b)acceleration if a=1,b=1,c=-2

(c) force if a=0,b=-1,c=–2

(d) pressure if a=1,b=-1,c= -2

Q33.Given that the displacement of an oscillating particle is given by y=Asin (Bx=a+D).The displacement formula for (ABCD)is:

(a)[M⁰L^-1T⁰]         (b)[M⁰L⁰T^-1]                                                                      (c)[M⁰L^-1T^-1]       (d)[M⁰L^OT⁰]

Q34. If force (F), work(w) and velocity (v) are taken as fundamental quantities ,then the dimensional formula of time (T)is:

(a)[WFv]                 (b)[WFv^-1]                                                                         (c)[W^-1F^-1v^-1]       (d)[WF^-1V^-1]

Q.35.The potential energy of a particle varies with distance x from a fixed origin as V=(A√x /(x+B)) where A and Bare constant ,The dimensions of AB are:

(a) [ML^5/2T^-2]         (b)[ML²T^-2]                                                                      (c)[ M^3/2L^3/2T^-2]    (d)[ML^7/2T^-2]

Q36.If force is proportional to square of velocity ,then the dimensions of proportionality constant is:

(a)[ML^-1T]                  (b)[ML^-1T⁰]                                                                       (c)[MLT⁰]                 (d)[M⁰LT^-1]

Q37.The speed (v) of ripples on the surface of water depends on surface tension (σ) ,density density (p) and wavelength (λ) The square of speed (v) is proportional to :

(a) σ/pλ    (b)p/σ λ       (c) λ/ pσ      (d)pσλ

Q38. The modulus of electricity is dimensionally equivalent to :

(a)strain                                      (b)force                  (c)stress                                      (d)coefficient of viscosity