If force can be represented as F = At + Bt 2 + D + x Cv where A, B, C, D are constant and F is force, v is velocity and x is distance. Then:

Question

If force can be represented as F = At + Bt 2 + D + x Cv ​ where A, B, C, D are constant and F is force, v is velocity and x is distance. Then:

TestHub · Accepted Answer

Every term on the RHS must have the dimension of force, $[M L T^{- 2}]$ .

$[A] = \frac{[ F ]}{[ t ]} = [M L T^{- 3}]$ - (A) is correct.

$[B] = \frac{[ F ]}{[ t ^{2} ]} = [M L T^{- 4}]$ , not $[M L T^{- 3}]$ . (B) is wrong.

D is added to x, so $[D] = [x] = [M^{0} L^{1} T^{0}]$ . (D) is correct.

$[C] = \frac{[ F ] [ D + x ]}{[ v ]}$

$= \frac{[ M L T ^{- 2} ] [ L ]}{[ L T ^{- 1} ]} = [M L T^{- 1}]$ , so C can be predicted. (C) is wrong.

Physics - Unit & Dimension Question with Solution | TestHub