Question

in a practical unit if the unit of mass becomes double and that of unit of time becomes half, then 8 joule will be equal to

Answer 1

8joules of work done can be expressed,as
work= 8 joules = 8kg m²/ s²
where normal units mass = kg
length= m
Time = second=s
let the new units be KG,M and S
According to question ,new mass is double that of initial value.
KG = 2kg
M= no change mentioned = so assume same = m
S= s/2
work =8 kg m/ s
=8 (KG/2)*M²/(2S)²
=8/8(KGM²/S²)
=1 Joule of work.

Answer 2

Joule = $kg * m^{2} / s^{2}$

Where kg is kilogram, m is meter and s is second.

Let new units be newJoule, newKg and newS.
Then formula for newJoule would be $newKg * m^{2} / (newS)^{2}$

According to the question newKg = 2kg i.e. 1kg = 1/2 * newKg
newS = s/2 i.e. 1s = 2 * newS

So 8 Joule = $8 * kg * m^{2} / s^{2}$
= $8 * (newKg /2 ) * m^{2} / (2 * newS) ^{2}$
=$(8 * 1/2 * 1/4 ) * newKg * m^{2} / newS^{2}$
= $1 * newKg * m^{2} / (newS)^{2}$
= 1 newJoule