JEE MainPhysicsUnits and Dimensions
The energy E of a particle is given by the empirical equation E = - x^2 t , where x is the distance and t is the time. If and are unknown constants, the dimensional formula of the product is :
Options
- A[M L^2 T⁻¹]
- B[M⁻¹ L^3 T]
- C[M⁻¹ L^2 T]
- D[M⁻¹ L^2 T^2]
Correct answer
C. [M⁻¹ L^2 T]
Step-by-step solution
According to the principle of homogeneity of dimensions, quantities added or subtracted must have the same dimensions. Therefore, the dimensions of must be equal to the dimensions of x^2 . [ ] = [L^2] The dimensional formula for energy is [E] = [M L^2 T⁻²] . From the given equation, we can write the dimensional equation as: [E] = [ ] [ ][t] [M L^2 T⁻²] = [L^2] [ ][T] [ ] = [L^2] [M L^2 T⁻²][T] = [M⁻¹ T] Now, the dimensional formula of the product is: [ ] = [L^2] [M⁻¹ T] = [M⁻¹ L^2 T] Answer: [M⁻¹ L^2 T]