Question

If S = at + bt² + c, S is displacement in meter and t is time in second then what is the dimensions of b?
1. LT^-1
2. L
3. LT^-2
4. L^-1T^-1

Answer 1

Correct Answer - Option 3 : 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, the velocity can be added to velocity but not to force.

EXPLANATION:

Given that:

S = at + bt2 + c

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

∴ [L] = [a] [T]

[a] = [LT^-1]

• Therefore the dimensions of 'a' is [LT-1].

For the second term,

⇒ [L] = [b] [T2]

[b] = [LT^-2]

• Therefore the dimensionS of 'b' is [LT-2].

Similarly [c] = [S] = [L]