Question

Find the value of 60 joule/minute on a system which has 100g, 100cm and 1min as fundamental units.

Answer 1

Answer:

$\frac{60 \text { joules }}{\min }=2.16 \times 10^{6} \ \text{in new unit}$

Given:

1 unit mass of defined system = 100 g

1 unit length of defined system = 100 cm

1 unit time of defined system = 1 min

Solution:

The fundamental units according to given question, the system is given with 100 g, 100 cm and 1 minutes. Unit conversion is required.

Thereby, 60 Joules per minute = n units

$\frac{60 \text { joules }}{\text { minutes }}=\mathrm{n}$

$\frac{60 \text { joules }}{60 \text { seconds }}=\mathrm{n}$

$\frac{1 \text { joules }}{\text { second }}=\mathrm{n}$

$\frac{1 \text { joules }}{\text { second }}=1 \mathrm{kg} \mathrm{m}^{2} \text { sec }^{-3}$

$1 \mathrm{kg} \mathrm{m}^{2} \sec ^{-1}=\mathrm{n}(100 \mathrm{g})(100 \mathrm{cm})^{2}(1 \mathrm{min})^{-3}$

$1\left(\frac{1 \mathrm{kg}}{100 \mathrm{g}}\right)\left(\frac{1 \mathrm{m}}{100 \mathrm{cm}}\right)^{2}\left(\frac{1 \mathrm{sec}}{1 \mathrm{min}}\right)^{-3}=\mathrm{n}$

$1\left(\frac{1000 \mathrm{g}}{100 \mathrm{g}}\right)\left(\frac{100 \mathrm{cm}}{100 \mathrm{cm}}\right)^{2}\left(\frac{1 \mathrm{sec}}{60 \mathrm{sec}}\right)^{-3}=\mathrm{n}$

$1(10 \mathrm{g})\left(\frac{1 \mathrm{sec}}{60 \mathrm{sec}}\right)^{-3}=\mathrm{n}$

$1(10 \mathrm{g})(60 \mathrm{sec})^{3}=\mathrm{n}$

$10 \times 216000=\mathrm{n}$

$2.16 \times 10^{6}=\mathrm{n}$

$\frac{60 \text { joules }}{\min }=2.16 \times 10^{6} \ \text{in new unit}$

Answer 2

Answer:

n = 2160000

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