NEETPhysicsUnits and Dimensions
The force F acting on a particle is given by the equation F = - x^2 t , where x is distance and t is time. The dimensional formula of the ratio is:
Options
- A[ M ⁻¹ L ^3 T ]
- B[ M L ^2 T ⁻²]
- C[ M L ⁻¹ T ⁻¹]
- D[ M L T ⁻¹]
Correct answer
D. [ M L T ⁻¹]
Step-by-step solution
According to the principle of dimensional homogeneity, quantities added or subtracted must have the same dimensions. Therefore, the dimensions of must be the same as those of x^2 . [ ] = [x^2] = [ L ^2] The dimensional formula for the entire equation is: [F] = [ ] [ ][t] Rearranging to find the dimensions of : [ ] = [ ] [F][t] = [ L ^2] [ M L T ⁻²][ T ] [ ] = [ L ^2] [ M L T ⁻¹] = [ M ⁻¹ L T ] Now, the dimensional formula of the ratio is: [ ] = [ L ^2] [ M ⁻¹ L T ] = [ M L T ⁻¹] Answer: [ M L T ⁻¹]