In two systems of units the relation between velocity - acceleration and force is v2 - -v1 e2 - - c - a2 - a1ec and F2 - -F1 - - ec where e and c are constants - what is the relation between mass -length and time in the two systems

First of all, F2=F1ec #8658;m2a2=m1a1ec #8658;m2a1ec=m1a1ec #8658;m2=m1ec2 Again, a2=a1ec #8658;dv2dt2=dv1dt1ec #8658;dt2dt1=1ecdv2dv1 Now nbsp; v2= ...

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Byju's Answer

Standard IX

Physics

Acceleration

in two system...

Question

in two systems of units the relation between velocity , acceleration and force is v₂ = (v₁ e² ) / c , a₂ = a₁ec and F₂ = (F₁) / ec where e and c are constants . what is the relation between mass ,length and time in the two systems

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Solution

First of all,
$F_{2} = \frac{F_{1}}{e c} \Rightarrow m_{2} a_{2} = \frac{m_{1} a_{1}}{e c} \Rightarrow m_{2} a_{1} e c = \frac{m_{1} a_{1}}{e c} \Rightarrow m_{2} = \frac{m_{1}}{{(e c)}^{2}}$
Again,
$a_{2} = a_{1} e c \Rightarrow \frac{d v_{2}}{d t_{2}} = \frac{d v_{1}}{d t_{1}} e c \Rightarrow \frac{d t_{2}}{d t_{1}} = \frac{1}{e c} \frac{d v_{2}}{d v 1}$
Now
$v_{2} = v_{1} \frac{e^{2}}{c} \Rightarrow \frac{d v_{2}}{d v_{1}} = \frac{e^{2}}{c}$
so,
$\frac{d t_{2}}{d t_{1}} = \frac{1}{e c} \frac{e^{2}}{c} = \frac{e}{c^{2}} \Rightarrow t_{2} = \frac{e}{c^{2}} t_{1} + t_{0}$
t₀is a constant.
Now
$v_{2} = \frac{v_{1} e^{2}}{c} \Rightarrow \frac{d l_{2}}{d t_{2}} = \frac{e^{2}}{c} \frac{d l_{1}}{d t_{1}} \Rightarrow d l_{2} = \frac{e^{2}}{c} \frac{d t_{2}}{d t_{1}} d l_{1} \Rightarrow d l_{2} = \frac{e^{2}}{c} \frac{e}{c^{2}} d l_{1} = \frac{e^{3}}{c^{3}} d l_{1} \Rightarrow l_{2} = \frac{e^{3}}{c^{3}} l_{1} + l_{0}$
l₀is a constant.

The answer is
$m_{2} = \frac{m_{1}}{{(e c)}^{2}} l_{2} = \frac{e^{3}}{c^{3}} l_{1} + l_{0} t_{2} = \frac{e}{c^{2}} t_{1} + t_{0}$

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in two systems of units the relation between velocity , acceleration and force is v2 = (v1 e2 ) / c , a2 = a1ec and F2 = (F1 ) / ec where e and c are constants . what is the relation between mass ,length and time in the two systems

in two systems of units the relation between velocity , acceleration and force is v₂ = (v₁ e² ) / c , a₂ = a₁ec and F₂ = (F₁) / ec where e and c are constants . what is the relation between mass ,length and time in the two systems