NEETPhysicsUnits and Dimensions
The displacement y of a particle in a medium is given by the equation y = A (bt - cx) , where t represents time and x represents distance. The dimensional formula for the ratio b c is:
Options
- A[M^0 L⁻¹ T]
- B[M^0 L^0 T^0]
- C[M^0 L⁻¹ T⁻¹]
- D[M^0 L T⁻¹]
Correct answer
D. [M^0 L T⁻¹]
Step-by-step solution
According to the principle of dimensional homogeneity, the argument of a trigonometric function must be dimensionless. Therefore, the quantities bt and cx are dimensionless. [bt] = [M^0 L^0 T^0] [b] = 1 [t] = [T⁻¹] [cx] = [M^0 L^0 T^0] [c] = 1 [x] = [L⁻¹] The ratio b c has the dimensions: [ b c ] = [T⁻¹] [L⁻¹] = [L T⁻¹] This corresponds to the dimensional formula [M^0 L T⁻¹] . Answer: [M^0 L T⁻¹]