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1.Units, Dimensions and Measurement
medium
Given that: $\lambda = a\,\cos \,\left( {\frac{t}{p} - qx} \right)$ , where $t$ represents time in second and $x$ represents distance in metre. Which of the following statements is true?
AThe unit of $x$ is same as that of $q$
BThe unit of $x$ is same as that of $p$
CThe unit of $t$ is same as that of $q$
DThe unit of $t$ is same as that of $p$
Solution
In $\cos \left(\frac{t}{p}-q x\right),$ the expression $\left(\frac{t}{p}-q x\right)$ is dimensionless. Hence, $t / p$ is also dimensionless. This is possible when units of $t$ are same as that of $p$.
Standard 11
Physics