Engineering Mechanics
The velocity ratio in case of an inclined plane inclined at angle 'θ' to the horizontal and weight being pulled up the inclined plane by vertical effort is

cosθ
sinθ
cosecθ
tanθ

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Engineering Mechanics
The loss of kinetic energy during inelastic impact, is given by (where m1 = Mass of the first body,m2 = Mass of the second body, and u1 and u2 = Velocities of the first and second bodies respectively.)

[2(m₁ + m₂)/m₁ m₂] (u₁ - u₂)²
[m₁ m₂/2(m₁ + m₂)] (u₁ - u₂)²
[m₁ m₂/2(m₁ + m₂)] (u₁² - u₂²)
[2(m₁ + m₂)/m₁ m₂] (u₁² - u₂²)

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Engineering Mechanics
The principle of transmissibility of forces states that, when a force acts upon a body, its effect is

Minimum, if it acts at the center of gravity of the body
Same at every point on its line of action
Different at different points on its line of action
Maximum, if it acts at the center of gravity of the body

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