The position of a particle at time t is given by the relation x(t)=((v0/α))(1-e-α t), where v0 is a constant and α0 The dimensions of v0 and a are respectively

Question

The position of a particle at time t is given by the relation x(t)=((v0/α))(1-e-α t), where v0 is a constant and α>0 The dimensions of v0 and a are respectively (A) M0 L1 T-1 and T-1 (B) M0 L1 T0 and T-1 (C) M0 L1 T-1 and L T-2 (D) M0 L1 T-1 and T

Tardigrade Admin · Accepted Answer

Dimension of α t=[M0 L0 T0] ∴[α]=[T-1] Again [(v0/α)]=[L] so [v0]=[L T-1]

Q. The position of a particle at time $t$ is given by the relation $x (t) = (\frac{v _{0}}{α}) (1 - e^{- α t})$ , where $v_{0}$ is a constant and $α > 0$ The dimensions of $v_{0}$ and a are respectively

$M^{0} L^{1} T^{- 1}$ and $T^{- 1}$

$M^{0} L^{1} T^{0}$ and $T^{- 1}$

$M^{0} L^{1} T^{- 1}$ and $L T^{- 2}$

$M^{0} L^{1} T^{- 1}$ and $T$

Dimension of $α t = [M^{0} L^{0} T^{0}]$
$∴ [α] = [T^{- 1}]$
Again $[\frac{v _{0}}{α}] = [L]$
so $[v_{0}] = [L T^{- 1}]$

Q. The position of a particle at time t is given by the relation x(t)=(αv0​​)(1−e−αt), where v0​ is a constant and α>0 The dimensions of v0​ and a are respectively

M0L1T−1 and T−1

M0L1T0 and T−1

M0L1T−1 and LT−2

M0L1T−1 and T