Question

The position of a particle at time 't' is given by the equation $x\left(t\right)=\frac{V_0}{A}(1-e^{17}).$ Where $V_0$ is constant and $A>0.$ Dimensions of $V_0$ and A respectively are

• A. $M^{0}L.T^0$ and $T^{-1}$
• B. $M^{0}L.T^{-1}$ and $L{T}^{-2}$
• C. $M^{0}L.T^{-1}$ and $T$
• D. $M^0.L.T^{-1}$ and $T^{-1}$

Answer 1

The correct option is D $M^0.L.T^{-1}$ and $T^{-1}$

$x\left(t\right)=\frac{v_0}{A}(1-e^{AT})$
Clearly, $A=T^{-1}$
& $\frac{V_0}{T}=L$ (length)
$\frac{V_0}{T^{-1}}=L$
$\therefore V_0=L{T}^{-1}$
$\therefore V_0=M^{0}L{T}^{-1}$
$A=T^{-1}$