Question

UMS & Measurements
Die b:
If unit of time is taken as 10 s, unit of mass 5 kg and unit of length 20 m, then convert 1 J
in new unit of energy.
​

Answer 1

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Answer 2

Given :-

• Unit of time taken is 10 s
• Unit of mass is 5 kg
• Unit of length is 20m

ToFind :-

• Convert 1 J in new unit of energy.

Solution :-

Dimensional formula of energy is $ml {}^{2} t {}^{ - 2}$

$n_{2} = \: n_{2}( \frac{ m_{ 1} }{ m_{2} } ) {}^{a} \: ( \frac{ l_{ 1} }{ l_{2} } ) {}^{b} \: ( \frac{ t_{ 1} }{ t_{2} } ) {}^{c}$

$n_{2} = \: 1 \: ( \frac{1kg }{ 5kg } ) {}^{2} \: ( \frac{ 1m }{ 20m} ) {}^{ 2} \: ( \frac{ 1s }{ 10s} ) {}^{ - 2}$

$n_{2} = \: \frac{1 \times 10 \times 10}{5 \times 20 \times 20}$

$n_{2} = \: \frac{1}{20} \: \: {\sf{new \: unit}}$

Thanks.