First slide

Dimensions of physical quantities

Question

$If F = \frac{v}{C \ln (x b)}, then$

Moderate

A

F and v denote force and velocity, the dimensions of $C are [M T]$
B

x denotes distance, the dimensions of b are $[L^{- 1}]$
C

the dimension of $\frac{v}{C}$ never be same as F
D

the dimensions of x must be same as $\frac{v}{c b}$

Solution

Logarithm has no dimensions.
$[x b] = [M^{0} L^{0} T^{0}] \Rightarrow [b] = [L^{- 1}]$
Hence, option (b) is correct.

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