If E and E_0 denote energies at time t and t_ | vedclass

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

Question

(D) Dimensional analysis requires that both sides of an equation have the same dimensions and that the argument of any exponential function must be di

Vedclass · Accepted Answer

$C, D$ only

Vedclass · Answer

(D) Dimensional analysis requires that both sides of an equation have the same dimensions and that the argument of any exponential function must be dimensionless.$(A) E = 2 E_0 \frac{L}{L_0}$$LHS$: $[M L^2 T^{-2}]$$RHS$: $[M L^2 T^{-2}] 	imes \frac{[L]}{[L]} = [M L^2 T^{-2}]$Status: Dimensionally correct.$(B) E = E_0 e^{-\frac{2 L}{L_0}}$Exponent: $\frac{[L]}{[L]} = [1]$ (Dimensionless). Correct.$LHS$: $[M L^2 T^{-2}]$$RHS$: $[M L^2 T^{-2}] 	imes [1] = [M L^2 T^{-2}]$Status: Dimensionally correct.$(C) E = 2 L e^{-\frac{L}{E_0}}$Exponent: $\frac{[L]}{[M L^2 T^{-2}]} = [M^{-1} L^{-1} T^2]$. Since the exponent is not dimensionless,the expression is invalid.$LHS$: $[M L^2 T^{-2}]$Pre-factor: $[L]$Status: Dimensionally incorrect.$(D) E = 2 \left( \frac{E_0}{L_0} ight) e^{-\frac{L}{L_0}}$Exponent: $\frac{[L]}{[L]} = [1]$. Correct.$LHS$: $[M L^2 T^{-2}]$$RHS$: $\frac{[M L^2 T^{-2}]}{[L]} = [M L T^{-2}]$Status: Dimensionally incorrect.Therefore,equations $(C)$ and $(D)$ are incorrect.

Similar Questions

The Martians use force $(F)$,acceleration $(A)$,and time $(T)$ as their fundamental physical quantities. The dimensions of length in the Martian system are:

In the equation $y = x^2 \cos^2 \left( 2 \pi \frac{\beta \gamma}{\alpha} \right)$,the units of $x, \alpha, \beta$ are $m, s^{-1}$,and $(ms^{-1})^{-1}$ respectively. The units of $y$ and $\gamma$ are:

The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?

The dimensions of the product $\mu_{0} \varepsilon_{0}$ are related to those of velocity as

If $E$ and $E_0$ represent the energies,and $t$ and $t_0$ represent the times,which of the following relations is dimensionally correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module