Question

If units in two systems of measurements are in the ratio 2:3,the ratio of the units of angular momentum in those two system is1. 2:32. 9:43. 1:14. 4:9

Answer 1

Answer:

4 : 9

Explanation:

angular momentum unit

In SI          U₁ = kg m^2 / s

In C G S   U₂ = g cm^2 / s

according to question units in two systems are in the ratio 2 : 3

2 U₁ : 3 U₂

=> (2 kg) (2 m)^2 / 2 s : (3 g) (3 cm)^2 / 3 s

=> 2 x 4 / 2 : 3 x 9 / 3

=> 4 : 9

                                       OR

Angular momentum = [ M L² T⁻¹ ]

U₁ = [ M₁ L₁² T₁⁻¹ ]

U₂ = [ M₂ L₂² T₂⁻¹ ]

U₁ : U₂ = $\frac{[M_{1} L^{2}_{1} T^{2}_{1} ]} {[M_{2} L^{2}_{2} T^{2}_{2} ]}$

          = $[\frac{M_{1} }{M_{2}}] [\frac{L_{1} }{L_{2}}]^{2} [\frac{T_{1} }{T_{2}}] ^{-1}$

according to question units in two systems are in the ratio 2 : 3

          = [2 / 3] [2 / 3]^2 [2 / 3]^-1

         = 4 / 9