IAT IISER2026PhysicsUnits and Dimensions
The acceleration of a point particle is given by the equation d^2 x dt^2 = x | x |^7 + d x dt where x denotes position and t denotes time. Which of the following relations show the correct dimensions for and ?
Options
- A[ ] = [M^1L^6T⁻²] , [ ] = [M^0L^0T⁻³]
- B[ ] = [M^0L^6T⁻¹] , [ ] = [M^0L^1T⁻²]
- C[ ] = [M^0L^7T⁻²] , [ ] = [M^0L^0T⁻¹]
- D[ ] = [M^0L^7T⁻²] , [ ] = [M^0L^0T^0]
Correct answer
C. [ ] = [M^0L^7T⁻²] , [ ] = [M^0L^0T⁻¹]
Step-by-step solution
According to the principle of dimensional homogeneity, each term in the equation must have the same dimensions. [ d^2 x dt^2 ] = [ x | x |^7 ] = [ d x dt ] Substituting the dimensions of position [L] and time [T] : [LT⁻²] = [ ] [L] [L^7] [ ] = [LT⁻²] [L^6] = [M^0L^7T⁻²] Similarly for : [LT⁻²] = [ ] [LT⁻¹] [ ] = [LT⁻²] [LT⁻¹] = [M^0L^0T⁻¹] Answer: [ ] = [M^0L^7T⁻²] , [ ] = [M^0L^0T⁻¹]