If the units of force, energy and velocity are 10 N, 100 J and 5 m/s then the unit of mass is :

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Physics

Dimensions

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Question

If the units of force, energy and velocity are 10 N, 100 J and 5 m/s then the unit of mass is :

2 kg

3 kg

4 kg

1 kg

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Force = [M¹L¹T⁻²] = F

Energy = [M¹L²T⁻²] = E

Velocity = [LT⁻¹] = V

M¹α,F^aE^bV^c

M′ = (M¹L¹T⁻²,)^a(M¹L²T⁻²,)^b(LT⁻¹)^c

1 = a + b, : ,b + c = −1, : ,c = −2,

0 = a + 2b + c, : ,−(2a + 2b) − c = 0, : ,b = 1

0 = −2a − 2b − c, : ,a = 0

$\Rightarrow Mass = \frac{Energy}{(Velocity)^{2}} = \frac{100}{(5)^{2}} = 4 kg$