Question

17. In a new system of units mass, acceleration and frequency are taken as fundamental units. If unit of mass is 100 g, unit of acceleration is 2 m/sand unit of frequency is 4 sec-' in the new system of units then find the value of 0.1 J in this system.​

Answer 1

Answer:

1N can be represented as kgm/s2 

1N=[T]2[M][L]=(1s)2(1Kg)(1m)=(51unitoftime)2(21unitofmass)(51unitoflength)=21×51×15×15unitofforce=25unitofforce.

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Answer 2

The value of 0.1 J in the new system is 4 unit

We know, in case of dimension and units,

nu = constant

Where n =  numerical value

u = unit used

Now, Joule is the unit of 'Work Done' and its dimension is ML²T⁻²

Now, mass(M), acceleration(a) and frequency (f) are taken as fundamental units.

According to this unit, the Work done will be written as Ma²f⁻²

It is derived according to the following,

ML²T⁻² = Mˣaᵇfⁿ

or, ML²T⁻² = Mˣ (LT⁻²)ᵇ (T⁻¹)ⁿ

or, ML²T⁻² = Mˣ Lᵇ T⁻²ᵇ⁻ⁿ

By comparing, we get,

x = 1 , b = 2 , and

-2b-n = -2

or, -4 - n = -2

or, n = -2

According to the above equation,

n₁u₁ = n₂u₂   , Where subscript 1 represents the new unit of system and 2 represents the previous system.

Now,

n₁/n₂ = u₂/u₁

∴ n₁/ 0.1 = (1000/100)× (1/2)² × (1/4)⁻² [ By using Ma²f⁻² ]

Or, n₁/ 0.1 = 10 × 0.25 × 16

or, n₁ = 0.1 × 10 × 0.25 × 16

or, n₁ = 4

So, in the new system of units then find the value of 0.1 J is 4 unit.