Correct Answer - Option 4 : kg m
-2
The correct answer is option 4) i.e. kg m-2
CONCEPT:
- The SI base units are the standard units of measurement.
-
The seven base units used in the SI system are meter (m), kilogram (kg), second (s), kelvin (K), ampere (A), mole (mol), and candela (cd).
- The seven base units along with their dimensions are as follows:
Fundamental quantity |
Dimension |
Time |
T |
Mass |
M |
Electric current
|
A |
Thermodynamic temperature |
K |
Amount of substance |
mol |
Luminous intensity |
cd |
Length |
L
|
EXPLANATION:
- The capacitance C is related to the charge Q and voltage V across them as: \(C =\frac{Q}{V}\)
- Dimensions of charge, Q = current × time = [A] × [T] = [A1T1]
- Dimensions of voltage, V = work done per unit charge = (force × displacement)(charge)-1 = [M1L1T-2][L1] × [A1T1]-1 = [M1L2A-1T-3]
- Dimensions of capacitance, \( C =\frac{[A^1T^1]}{[M^1L^2A^{-1}T^{-3}]} = [M^{-1}A^2L^{-2}T^4]\)
- A charged particle (q) moving with a speed (v) relative to a magnetic field experiences a magnetic force due to the magnetic field (B). The magnitude of this force (F) is given by
F = qvB
- Magnetic field intensity, \(B =\frac{F}{qv}\)
- Dimensions of force, F = [M1L1T-2]
- Dimensions of charge, q = [A1T1]
- Dimensions of velocity, v = [L1T-1]
- Dimensions of \(B =\frac{[M^1L^1T^{-2}]}{[A^1T^{1}][L^1T^{-1}]} = [M^1T^{-2}A^{-1}]\)
⇒ Dimension of x = CB2 = [M-1A2L-2T4] [M1T-2A-1]2 = [M1L-2]
⇒ SI base unit for [M] and [L] is kg and m respectively.
⇒ [M1L-2] = kg m-2