If the units of force, energy and velocity ar | vedclass

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Question

The Dimensional formulae of
force $=\left[\mathrm{ML} T^{-2}\right]$
energy $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2}\right]$
velocity $=\left[\mathr

Vedclass · Accepted Answer

$10\, m, 4 \,kg, 2\, sec$

Vedclass · Answer

The Dimensional formulae of
force $=\left[\mathrm{ML} T^{-2}ight]$
energy $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2}ight]$
velocity $=\left[\mathrm{L} T^{-1}ight]$
Thus We have
$\left[\mathrm{ML} T^{-2}ight]=10 \mathrm{N} \ldots \ldots . .(\mathrm{i})$
$\left[\mathrm{ML}^{2} \mathrm{T}^{-2}ight]=100 \mathrm{J} \ldots . .(\mathrm{ii})$
$[\mathrm{LT}-1]=5 \mathrm{ms}^{-1} \ldots \ldots .$ (iii)
and
Dividing equation (ii) by eq.(i) ,we have
$[\mathrm{L}]=100 \mathrm{J} / 1 \mathrm{0N}=10 \mathrm{0Nm} / 1 \mathrm{0N}=1 \mathrm{0m}$
Substituting the unit of $[\mathrm{L}]$ in eq. (iii) $,$ we have
$[\mathrm{T}]=10 \mathrm{m} / 5 \mathrm{ms}^{-1}=2 \mathrm{s}$
Substituting the units of $[\mathrm{L}]$ and $[\mathrm{T}]$ in eq.( i) we have
$[\mathrm{M}]=10 \mathrm{N} /[\mathrm{L}]\left[\mathrm{T}^{-2}ight]=10 \mathrm{N} 	imes 4 \mathrm{s}^{2} / 10 \mathrm{m}=4 \mathrm{kg}$

If the units of force, energy and velocity are respectively $10\, N, 100\, J, 5\, m/s$, then the units of length, mass and time will be

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