Question

find the value of 10 joules on a system which has 10cm, 100g, and 30 sec as the fundamental units

Answer 1

1J = 1 kg * m^2 * s^-2
10J = 10 kg * m^2 * s^-2
10J = 10 * 1000g * (100cm)^2 * [30/(30cm)]^2
10J = 10 * 10(100g) * 100(10cm)^2 * 900(1/30s)^2
10J = 9000000 * {100g * 100cm^2 * (1/900s^2)}

Answer 2

Answer:

The value of 10J is $\bold{9 \times 10^{6}}$

Explanation:

Kinetic energy is the energy that an object has due to its motion. It is represented as the $\bold{\mathrm{E}_{\mathrm{k}}=\frac{1}{2} m v^{2}}$ where $E_{k}$ Kinetic Energy, m = Mass of an object, v= Velocity of the object

The unit of Kinetic Energy is Joule. Now we will write Joule in terms of new units as asked.

As per the requirement, new units are as follow -  

L = 10 cm, M = 100 g, T= 30 s

E = 10 Joule  $=\frac{1}{2} m v^{2}=10 \mathrm{Kg}(\mathrm{m} / \mathrm{s})^{2}$

$\begin{array}{l}{10 \mathrm{J}=10 \mathrm{Kg}(\mathrm{m} / \mathrm{s})^{2}=10 \times 1000 \mathrm{g} \times(100 \mathrm{cm} / \mathrm{s})^{2}} \\ {=10 \times 10 \times(100 \mathrm{g}) \times(10 \times 10 \mathrm{cm} / \mathrm{s})^{2}}\end{array}$

$\begin{array}{l}{=100 \times(100 \mathrm{g}) \times(10 \times 30 \times 10 \mathrm{cm} / 30 \mathrm{s})^{2}} \\ {=100 \times(100 \mathrm{g}) \times(300 \times 10 \mathrm{cm} / 30 \mathrm{s})^{2}} \\ {=100 \times(300) 2 \times(100 \mathrm{g})(10 \mathrm{cm} / 30 \mathrm{s})^{2}}\end{array}$

$\begin{aligned} &=9 \times 10^{6} \times 100 g(10 \mathrm{cm} / 30 \mathrm{s})^{2} \\ &=9 \times 10^{6} \text { fundamental unit } \end{aligned}$