Question

The displacement of a particle moving along $x$-axis with respect to time $t$ $x=at+bt^{2}+ct^{3}$ . The dimensions of $c$ are

• A. $T^{-3}$
• B. $LT^{-2}$
• C. $LT^{-3}$
• D. $LT^{3}$

Answer 1

Answer: (C)

$LT^{-3}$

Answer 2

The displacement of a particle moving along $x$ -axis with respect to time $t$
$x=a t+b t^{2}-c t^{3}$
Dimension of $c t^{3}=$ Dimension of $x$
$\left[c t^{3}\right]=[x]$
or $[c]=\frac{[ L ]}{\left[ T ^{3}\right]}$
Dimensions of $c=\left[ LT ^{-3}\right]$