Question

In a new set of units, unit of mass is 10 kg, unit of length is 1 km and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is

Answer 1

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The correct answer is

3.6
×
10
−
4
new units

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Answer 2

Answer:

The value of 1 joule in this new hypothetical system is $3.6\times10^{-4}\ J$.

Explanation:

Given that,

In a new set of units

M = 10 kg

L = 1 km

T = 1 m

Let us consider n₁ and n₂ is the S.I unit and unit of new system.

$n_{1}=1\ J$

The value of 1 joule of the new set

The dimension formula of Joule is

$F = [ML^2T^{-2}]$

S.I unit of energy = new system

$n_{1}([M_{1}L_{1}^{2}T_{1}^{-2}])=n_{2}([M_{2}L_{2}^{2}T_{2}^{-2}])$

$\dfrac{n_{2}}{n_{1}}=(\dfrac{M_{1}}{M_{2}}) (\dfrac{L_{1}}{L_{2}})^{2} (\dfrac{T_{1}^{-2}}{T_{2}^{-2}})$

$\dfrac{n_{2}}{n_{1}}=(\dfrac{1}{10})\times(\dfrac{1}{1000})^{2}\times(\dfrac{1}{60})^{-2}$

$\dfrac{n_{2}}{n_{1}}=\dfrac{36}{100000}$

$n_{2}=1\times3.6\times10^{-4}\ J$

$n_{2}=3.6\times10^{-4}\ J$

Hence, The value of 1 joule in this new hypothetical system is $3.6\times10^{-4}\ J$.