First slide

Dimensions of physical quantities

Question

Write the dimensions of a x b in the relation $E = \frac{b - x^{2}}{a t}$ where E is the energy, x is the displacement, and t is the time.

Moderate

A

$M L^{2} T$
B

$M^{- 1} L^{2} T^{1}$
C

$M L^{2} T^{- 2}$
D

$M L T^{- 2}$

Solution

$\begin{array}{l} Here, b and x^{2} = L^{2} have same dimensions. \\ Also, a = \frac{L^{2}}{E \times t} = \frac{L^{2}}{(M L^{2} T^{- 2}) T} = M^{- 1} T^{1} \\ a \times b = [M^{- 1} L^{2} T^{1}] \end{array}$

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