Question

In a new system of units, unit of mass is 2 kg, unit of length is 4 m and unit of time is 2 second. How much joule is equal to 1 unit of energy in this new system?​

Answer 1

Answer:$E= \frac{ML^2}{T^{2}}$

$= \frac{2 Kg\times 4^2 m^2}{2^2 s^2}\\\\= \frac{32}{4}\frac{Kgm^2}{s^2}\\=8 \frac{Kgm^2}{s^2}$

1 unit of energy = 8 J

Explanation: Energy, $E=\frac{1}{2}mv^2$

The SI unit of Energy is the joule (J), which is equal to $Kgm^2/s^2$So the dimensional formula for Energy is $ML^2T^{-2}$

Where,

M=Mass

L = length

T= time

For the New system of units,

unit of mass = 2 Kg

unit of  length = 4 m

unit of time = 2 s