NEETPhysicsUnits and Dimensions
The mechanical power P delivered to a particle depends on time t and position x according to the equation P = - t^2 x . The dimensions of the product ( ) are:
Options
- A[ M ⁻¹ ~L ⁻³ ~T ^7]
- B[ M ⁻¹ ~L ⁻³ ~T ^6]
- C[ M ⁻¹ ~L ⁻³ ~T ^5]
- D[ M L ^3 ~T ⁻³]
Correct answer
A. [ M ⁻¹ ~L ⁻³ ~T ^7]
Step-by-step solution
According to the principle of homogeneity of dimensions, quantities added or subtracted must have the same dimensions. From the numerator ( - t^2) , we have: [ ] = [t^2] = [ T ^2] The dimensional formula for power P is [ M L ^2 ~T ⁻³] . Substituting the dimensions into the given equation P = - t^2 x : [ M L ^2 ~T ⁻³] = [ T ^2] [ ] [ L ] Rearranging for [ ] : [ ] = [ T ^2] [ M L ^2 ~T ⁻³] [ L ] = [ T ^2] [ M L ^3 ~T ⁻³] = [ M ⁻¹ ~L ⁻³ ~T ^5] The dimensions of the product ( ) are: [ ] = [ T ^2] [ M ⁻¹ ~L ⁻³ ~T ^5] =