The quantity with the same units as force times time,Ft,with dimensions MLT ^- ¹ is A)mv B)mvr C)mv²r D)ma E) $\frac { m v ^ { 2 } } { r }$

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The given dimensions for Ft are: MLTF1F1F1S1^F1F1F10¹ Notice that the dimensions for force are MLT-2 (mass, length, time^-2) and the dimensions for time are T (time). Multiplying these yields MLT-1. Therefore, Ft has dimensions of MLT-1 multiplied by T, resulting in the dimensions MLT^2. The only choice with these same dimensions is A) mv. The dimensions for m are M (mass) and the dimensions for velocity are LT^-1 (length, time^-1), so multiplying these yields MLT^-1, which when multiplied by time T, results in MLT^2, the same dimensions as Ft.

The Quantity with the Same Units as Force Times Time,Ft,with mv2r\frac { m v ^ { 2 } } { r }rmv2​

The Quantity with the Same Units as Force Times Time,Ft,with $\frac { m v ^ { 2 } } { r }$