Question

Find the value of 10 joule in a system When mass is 1kg length 10 cm and time 5 min.

Answer 1

One unit mass=1kg
One unit length=10cm
One unit time =5min
Therefore;
10joule=X units
10kg m2 s-2=Xkg(10cm)2(5min)-2
10kg m2 s-2=X(1/9000000)kg m2 s-2
10*9000000=X

Answer 2

According to given question, the system is given with 1 kg, 10 cm and 5 minutes. Unit conversion is required.

Given, 1 unit mass of defined system = 1 kg

1 unit length of defined system = 10 cm

1 unit time of defined system = 5 min.

Thereby, 10 Joules = n units

$\begin{array}{l}{10 \text { joules }=10 \mathrm{kg} \mathrm{m}^{2} \mathrm{sec}^{-2}} \\ {10\ \mathrm{kg} \mathrm{m}^{2} \sec ^{-2}=\mathrm{n}(1 \mathrm{kg}) \times(10 \mathrm{cm})^{2} \times(5 \mathrm{min})^{-2}}\end{array}$

$10\left(\frac{1 k g}{1 k g}\right) \times\left(\frac{1 m}{10 c m}\right)^{2} \times\left(\frac{1 s e c}{5 \min }\right)^{-2}=n$

$10\left(\frac{100 \mathrm{cm}}{10 \mathrm{cm}}\right)^{2} \times\left(\frac{1 \mathrm{sec}}{5 \times 60 \mathrm{sec}}\right)^{-2}=n$

$10(10 \mathrm{cm})^{2} \times\left(\frac{1 \mathrm{sec}}{300 \mathrm{sec}}\right)^{-2}=n$

$\begin{array}{c}{10(10 \mathrm{cm})^{2} \times(300 \mathrm{sec})^{-2}=n} \\ {10 \times 100 \times 90000=n} \\ {9 \times 10^{7}=n} \\ {10 \text {joules}=9 \times 10^{7}}\end{array}$