Theory of Machine
A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by (where μ = tan φ = Coefficient of friction between the plane and the body)

P = W tan (α + φ)
P = W (cos α + μ sin α)
P = W (sin α + μ cos α)
P = W tan α

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Theory of Machine
A thin circular disc is rolling with a uniform linear speed, along a straight path on a plane surface. Which of the following statement is correct in this regard?

The centre of the disc has centrifugal acceleration
All points of the disc have the same velocity
The centre of the disc has zero acceleration
The point on the disc making contact with the plane surface has zero acceleration

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

l₁ + l₂ + l₃
(l₁ + l₂ + l₃)/3
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴

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Theory of Machine
In a cam drive with uniform velocity follower, the sharp corners of the displacement diagram are rounded off at the beginning and at the end of each stroke. This is done

In order to have acceleration in beginning and retardation at the end of stroke within the finite limits
Because of difficulty in manufacturing cam profile
Because of loose contact of follower with cam surface
Because the uniform velocity motion is a partial parabolic motion

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