Velocity (v) and acceleration (a) in two syst | vedclass

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

Question

(B) Given: $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{mn}$.Since $v = \frac{L}{T}$ and $a = \frac{L}{T^{2}}$,we have:$\frac{L_{2}}{T_{2

Vedclass · Accepted Answer

$L_{1} = \frac{n^{4}}{m^{2}} L_{2}$ and $T_{1} = \frac{n^{2}}{m} T_{2}$

Vedclass · Answer

(B) Given: $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{mn}$.Since $v = \frac{L}{T}$ and $a = \frac{L}{T^{2}}$,we have:$\frac{L_{2}}{T_{2}} = \frac{n}{m^{2}} \frac{L_{1}}{T_{1}}$  --- $(1)$$\frac{L_{2}}{T_{2}^{2}} = \frac{1}{mn} \frac{L_{1}}{T_{1}^{2}}$ --- $(2)$Dividing $(1)$ by $(2)$:$\frac{T_{1}^{2}}{T_{2}} = \frac{n}{m^{2}} 	imes mn 	imes T_{1} = \frac{n^{2}}{m} T_{1}$$\frac{T_{2}}{T_{1}} = \frac{m}{n^{2}}$ (This implies $T_{1} = \frac{n^{2}}{m} T_{2}$).Substituting $T_{2} = \frac{m}{n^{2}} T_{1}$ into $(1)$:$\frac{L_{2}}{(\frac{m}{n^{2}}) T_{1}} = \frac{n}{m^{2}} \frac{L_{1}}{T_{1}}$$L_{2} = \frac{n}{m^{2}} 	imes \frac{m}{n^{2}} L_{1} = \frac{1}{mn} L_{1}$$L_{1} = mn L_{2}$.Checking the options,the correct relation for time is $T_{1} = \frac{n^{2}}{m} T_{2}$.

Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{mn}$ respectively. Here $m$ and $n$ are constants. The relations for distance $(L)$ and time $(T)$ in the two systems are:

Similar Questions

If $10 \ g \ cm \ s^{-1} = x \ N \ s$,then the number $x$ is

The velocity of water waves $v$ may depend upon their wavelength $\lambda$,the density of water $\rho$,and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as:

In Vander Waal's equation $\left[ P + \frac{a}{V^2} \right] (V - b) = RT$,the dimensions of $a$ are

The velocity of a freely falling body changes as ${g^p}{h^q}$ where $g$ is the acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module