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  4. Two quantities A and B are related by the relation (A/B) =m , where m is linear mass density and A is force. The dimensions of B will be

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Q. Two quantities $A$ and $B$ are related by the relation $\frac{A}{B}$ $=m$ , where $m$ is linear mass density and $A$ is force. The dimensions of $B$ will be

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

$\left[B\right]=\frac{\left[A\right]}{\left[m\right]}$
$\left[B\right]=\left[\frac{force}{mass / length} \, \right]$
$\left[\text{B}\right]=\left[\frac{force \times length}{mass}\right]=\left[\frac{energy}{mass}\right]=$ $\left[\right.latentheat\left]\right.$