The position of a particle at time t is given | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, the exponent of the exponential function must be dimensionless. Therefore, the dimensions of

Vedclass · Accepted Answer

$[M^0 LT^{-1}]$ and $[M^0 L^0 T^{-1}]$

Vedclass · Answer

(D) In the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, the exponent of the exponential function must be dimensionless. Therefore, the dimensions of $At$ must be $[M^0 L^0 T^0]$.Since $[t] = [T]$, we have $[A][T] = [1]$, which implies $[A] = [T^{-1}] = [M^0 L^0 T^{-1}]$.Next, the term $(1 - e^{-At})$ is dimensionless. Thus, the dimensions of $x$ must be equal to the dimensions of $\frac{v_0}{A}$.$[x] = \frac{[v_0]}{[A]} \implies [L] = \frac{[v_0]}{[T^{-1}]}$.Therefore, $[v_0] = [L][T^{-1}] = [M^0 LT^{-1}]$.Thus, the dimensions of $v_0$ and $A$ are $[M^0 LT^{-1}]$ and $[M^0 L^0 T^{-1}]$ respectively.

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

Similar Questions

The dimensional formula for the intensity of radiation is .......

Write the dimensional formula for energy density.

An object is moving through a liquid. The viscous damping force acting on it is proportional to its velocity. The dimension of the constant of proportionality is:

The dimensional formula of $\frac{B^2}{2\mu_0}$ is . . . . . . .

The dimensional formula for latent heat is

Vedclass Test Series

Exam Paper Generator

Online Exam Module