Question

In a new system of units, unit of mass is 100 g, unit of length is 4 m and unit of time is 2 s . Find the numerical value of 10 J in this system.

Answer 1

Explanation:

Solution :

`IN=x "units"`

`x=((1"kg")/(10"kg"))((1"m")/(100"m"))((1"sec")/(60"sec"))^(-2)=(1)/(10)xx(1)/(100)xx3600`

`x=3.6`

Answer 2

Given:

• Unit of mass = 1000Kg
• Unit of length = 4m
• Unit of time = 2s

To Find:

• The numerical value of 10J

Solution:

Since we need to find the numerical value of 10J, the Unit of energy is used.

We know that,

Energy = M$L^2$$T^{-2}$

1 Unit of energy = [M*$L^2$]/$T^2$ → {equation 1}

On substituting the given values in equation 1 we get,

⇒ 1 unit of energy = (100/1000)*4*4)/2*2

In the above step, we converted grams into kilograms by dividing the mass value by 1000

⇒ 1 unit of energy = (1/10*16)/4 = (16/10)/4 {dividing the terms}

⇒ 1 unit of energy = 4/10 J

⇒ 1 J = 4/10 unit of energy {dividing the terms}

⇒ 10J = 100/4 unit of energy = 25 units.

∴ The numerical value of 10J = 25 units.