Question 77: Units , Dimensions and Error Analysis

Question

Match List I with List II

LIST I

LIST II

A.
Torque
I.
$$\left[M^1 L^1 T^{-2} A^{-2}\right]$$

B.	
Magnetic field
II.
$$\left[L^2 A^1\right]$$

C.
Magnetic moment
III.
$$\left[M^1 T^{-2} A^{-1}\right]$$

D.
Permeability of free space
IV.
$$\left[M^1 L^2 T^{-2}\right]$$

Choose the correct answer from the options given below:

Accepted Answer

To determine the correct matches between List I and List II, we need to consider the dimensional formulas of the given physical quantities.
Torque (ÃÂ) is defined as the product of force (F) and distance (d):
$ 	au = F \cdot d $
The dimensional formula for torque is:
$ [	au] = [M^1 L^2 T^{-2}] $
Thus, Torque corresponds to IV.
Magnetic field (B) is derived from the relation involving force (F), charge (q), and velocity (V):
$ F = qVB $
The dimensional formula for the magnetic field is:
$ [B] = [M^1 T^{-2} A^{-1}] $
Thus, Magnetic field corresponds to III.
Magnetic moment (M) is the product of current (I) and area (A):
$ M = I \cdot A $
The dimensional formula for the magnetic moment is:
$ [M] = [L^2 A^1] $
Thus, Magnetic moment corresponds to II.
Permeability of free space (ÃÂ¼Ã¢ÂÂ) has the dimensional formula:
$ [ÃÂ¼Ã¢ÂÂ] = [M^1 L^1 T^{-2} A^{-2}] $
Thus, Permeability of free space corresponds to I.
Based on the above analysis, the correct matches are:
A. Torque Ã¢ÂÂ IV
B. Magnetic Field Ã¢ÂÂ III
C. Magnetic Moment Ã¢ÂÂ II
D. Permeability of free space Ã¢ÂÂ I
Therefore, the correct option is Option D:
A-IV, B-III, C-II, D-I.

Answer

A-I, B-III, C-II, D-IV

Answer

A-IV, B-II, C-III, D-I

Answer

A-III, B-I, C-II, D-IV

Answer

A-IV, B-III, C-II, D-I

Units , Dimensions and Error Analysis

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