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Dimensional Analysis

If velocity v...

Question

If velocity v is given as v = a + bx + ct where a, b and c are constant and x and t are position and time, then which of the following is dimentionally correct?

c = a b

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a = c b

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b = a c

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a^{2} = b c

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Solution

The correct option is A $c = a b$
Dimension of a is $[L T^{- 1}]$
of b is $[T^{- 1}]$
of c is $[L T^{- 2}]$
$a \times b = L T^{- 2}$
So, $a b$ can be equal to $c$ .

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