The dimensional formula for the product of two physical quantities $P$ and $Q$ is ${M L}^{2} T^{- 2}$ The dimensional formula of $\frac{P}{Q}$ is ${M T}^{- 2}$ . Then P and Q respectively are:

Force and velocity

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Momentum and displacement

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Force and displacement

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Work and velocity

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Solution

The correct option is B Force and displacement
$P \times Q = {M L}^{2} T^{- 2}$

$\frac{P}{Q} = {M T}^{- 2}$
$L e t : P = M^{A} l^{B} T^{C}$ and $Q = M^{a} l^{b} T^{c}$

$P \times Q = M^{A + a} l^{B + b} T^{C + c} = M^{1} l^{2} T^{- 2}$
$A + a = 1; B + b = 2; C + c = - 2$

$\frac{P}{Q} = M^{A - a} l^{B - b} T^{C - c} = {M T}^{- 2}$
$A - a = 1; B - b = 0; C - c = - 2$

$\Rightarrow A = 1, a = 0 B = b = 1, C = - 2, c = 0$

$S o, P = {M l T}^{- 2} \to f o r c e$
$Q = M^{0} l^{1} T^{0} \to d i s p l a c e m e n t$

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