Theory of Machine
The frequency of oscillation of a compound pendulum is

2π. √[(kG² + h²)/gh]
(1/2π). √[(kG² + h²)/gh]
2π. √[gh/(kG² + h²)]
(1/2π). √[gh/(kG² + h²)]

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Theory of Machine
Which of the following property of the instantaneous center is correct?

The velocity of the instantaneous centre relative to any third rigid link is same whether the instantaneous centre is regarded as a point on the first rigid link or on the second rigid link.
The two rigid links have no linear velocity relative to each other at the instantaneous centre.
A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
All of these

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Theory of Machine
The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r cosθ
m.ω².r sinθ
m.ω².r (sin 2θ/n)
m.ω².r (cos 2θ/n)

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