Question

Find the value of 20 J on the system based on 20 cm, 1kg and ½ minute as fundamental units.

Answer 1

Answer:

Steps and Understanding :

1) Let the new units be L, M, T where

1 L = 20 cm

1 M = 1 kg

1 T = 30 s

2) Now,

1 m = 10L

1 Kg = 1 M

1 s = 1/30 T

3) We have,

20 J = 20 kg m^2/s^2

= 20 \: kg \: \frac{ {m}^{2} }{ {s}^{2} } \\ = 20 \times 1 M\: \times \frac{ {(10L)}^{2} }{ { (\frac{1}{30} T)}^{2} } \\ = 20 \times 1 \times {10}^{2} \times {30}^{2} \\ = 18 \times {10}^{5} \: units \:

Answer 2

The answer is 4.5 × 10⁵

GIVEN

Numerical value Of energy = 20J

New system of units = 20 cm, 1kg and ½ minute.

TO FIND

The value of energy in new system.

SOLUTION

We can simply solve the above problem as follows;

We know that,

Dimensional formula of Energy = [ML²T⁻²]

Applying the formula:

n₁v₁ = n₂v₂

Where,

n₁ and n₂ are the numerical values in respective system of units.

And,

v₁ and v₂ are the respective fundamental units.

Therefore,

n₂ = n₁ × [M₁/M₂] × [L₁/L₂]² × [T₁/T₂]⁻²

= 20 × [1kg/Kg] × [1m/20cm]² × [1s/30s]⁻²

= 20 × [100/20]² × [30]²

= 20 × 5² × 30²

= 450000

n₂ = 4.5 × 10⁵

Hence, The answer is 4.5 × 10⁵

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