NEETPhysicsUnits and Dimensions
The velocity v of a particle depends upon its position x according to the equation v = A x + B x^2 . If v represents velocity and x represents distance, what is the dimensional formula for the product of the constants A and B ?
Options
- A[M^0 L^ -5/2 T^0]
- B[M^0 L^3 T⁻²]
- C[M^0 L^ 5/2 T⁻²]
- D[M^0 L^ 7/2 T⁻²]
Correct answer
D. [M^0 L^ 7/2 T⁻²]
Step-by-step solution
According to the principle of homogeneity of dimensions, each term in an equation must have the same dimensional formula. Given equation: v = A x + B x^2 The dimensions of velocity v are [L T⁻¹] and distance x are [L] . Equating dimensions of the first term to v : [A x ] = [v] [A] [L^ 1/2 ] = [L T⁻¹] [A] = [L T⁻¹] [L^ 1/2 ] = [L^ 1/2 T⁻¹] Equating dimensions of the second term to v : [ B x^2 ] = [v] [B] [L^2] = [L T⁻¹] [B] = [L T⁻¹] [L^2] = [L^3 T⁻¹] Now, finding the dimensional formula for the product A B : [A B]