Q122 / 160 · TS EAMCET 2016 · Physics
Force is given by the expression, $F=A \cos (B x)+C \cos (D t)$, where $x$ is displacement and $t$ is time. The dimension of $\left(\frac{D}{B}\right)$ is same as that of
- Correct answerAvelocity
- Bvelocity gradient
- Cangular velocity
- Dangular momentum
Solution
From dimension logic, the quantities of same dimensions can be added or subtracted, so
$\begin{aligned}<br />& {[B \mathrm{X}]=[D t] \text { similarly, } } \\<br />& \Rightarrow \left[\frac{x}{t}\right]=\left[\frac{D}{B}\right] \Rightarrow\left[\frac{D}{B}\right]=\frac{[\mathrm{L}]}{[T} \\<br />& \Rightarrow \text { Dimension of } \frac{D}{B}=\left[\mathrm{LT}^{-1}\right]<br />\end{aligned}$
$\left[L T^{-1}\right]$ is the dimension of velocity.
$\begin{aligned}<br />& {[B \mathrm{X}]=[D t] \text { similarly, } } \\<br />& \Rightarrow \left[\frac{x}{t}\right]=\left[\frac{D}{B}\right] \Rightarrow\left[\frac{D}{B}\right]=\frac{[\mathrm{L}]}{[T} \\<br />& \Rightarrow \text { Dimension of } \frac{D}{B}=\left[\mathrm{LT}^{-1}\right]<br />\end{aligned}$
$\left[L T^{-1}\right]$ is the dimension of velocity.
Hence, the correct answer is option: 'A'.