The velocity ν of a particle at time t is given by ν = a t + t + c b , where a , b and c are constants. The dimension of a , b and c are, respectively

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The velocity ν of a particle at time t is given by ν = a t + t + c b ​ , where a , b and c are constants. The dimension of a , b and c are, respectively

TestHub · Accepted Answer

According to the principle of homogeneity of dimensions, each term in the equation must have the same dimensions.

The dimension of velocity $ν$ is $[L T^{- 1}]$ .

For the term $a t$ , we have $[a] [T] = [L T^{- 1}]$ , which gives $[a] = [L T^{- 2}]$ .

In the term $\frac{b}{t + c}$ , the quantity $c$ is added to time $t$ , so $c$ must have the dimension of time. Thus, $[c] = [T]$ .

The dimension of the entire term $\frac{b}{t + c}$ must be equal to the dimension of velocity. Therefore, $\frac{[ b ]}{[ T ]} = [L T^{- 1}]$ , which gives $[b] = [L]$ .

The dimensions of $a, b$ , and $c$ are $L T^{- 2}, L$ , and $T$ respectively.

Answer: $L T^{- 2}, L, T$

Physics - Unit & Dimension Question with Solution | TestHub

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