Question

The position (x) of a car varies with time (t) as x = pt² + q. Find the dimensions of p. (Here x is in m, t is in second, p and q are constants)
1. LT^-1
2. LT^-2
3. L²T^-2
4. L^-2T

Answer 1

Correct Answer - Option 2 : LT^-2

CONCEPT:

• Principle of homogeneity of dimensions: According to this principle, a physical equation will be dimensionally correct if the dimensions of all the terms occurring on both sides of the equation are the same.
  • This principle is based on the fact that only the physical quantities of the same kind can be added, subtracted, or compared.
  • Thus, velocity can be added to velocity but not to force.

EXPLANATION:

Given that:

x = pt2 + q

• From the principle of dimensional homogeneity, the left-hand side of the equation dimensionally equal to the right-hand side of the equation.
• The dimension formula of position (x) = [L]

∴ [L] = [p] [T²]

[p] = [LT^-2]

• Therefore the dimensions of 'p' is [LT-2].

For the second term,

⇒ [L] = [q]