The power P delivered by a machine varies with distance x and time t according to the equation P = x + t^2 , where and are dimensional constants. The dimensional formula for the quantity ^2 is:

Step-by-step solution

From the principle of homogeneity of dimensions, the quantity must have the same dimensions as t^2 . [ ] = [ T ^2] The dimensional formula for power P is [ M L ^2 T ⁻³] and for distance x is [ L ] . Using the given equation P = x + t^2 , the dimensions of are: [ ] = [P][ + t^2] [ x ] [ ] = [ M L ^2 T ⁻³][ T ^2] [ L ^ 1/2 ] = [ M L ^ 3/2 T ⁻¹] The dimensional formula for ^2 is: [ ^2 ] = [ M L ^ 3/2 T ⁻¹]^2 [ T ^2] [ ^2 ] = [ M ^2 L ^3 T ⁻²] [ T ^2] = [ M ^2 L ^3 T ⁻⁴] Answer: [ M ^2 L ^3 T ⁻⁴ ]