Theory of Machine
Which of the following disciplines provides study of inertia forces arising from the combined effect of the mass and the motion of the parts?

Mechanisms
Applied mechanics
Kinetics
Theory of machines

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Theory of Machine
In a band and block brake, the ratio of tensions on tight side and slack side of the band is (where μ = Coefficient of friction between the blocks and the drum, θ = Semi-angle of each block subtending at the center of drum, and n = Number of blocks)

T₁/T₂ = [(1 + μ tanθ)/(1 - μ tanθ)]n
T₁/T₂ = [(1 - μ tanθ)/(1 + μ tanθ)]n
T₁/T₂ = μ. θ. n
T₁/T₂ = (μ θ)n

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Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

S₁/S₂ = r₁/r₂
(m.g + S₁)/(m.g + S₂) = r₁/r₂
(m.g - S₁)/(m.g - S₂) = r₂/r₁
S₂/S₁ = r₁/r₂

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