In the given figure, considering PN as one shaft, If the mass moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a rotor at P?

the given figure, considering left end has one rotor, If the mass moment of inertia of the shaft till node N1 is increased to four times, then what will be the effect on free torsional vibrations of a rotor at left end of N1?

A

Increases 4 times

B

Increases 2 times

C

Decreases 4 times

D

Decreases 2 times

The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft and $$I$$ = Mass moment of inertia of the disc attached at the end of a shaft)

A

$$2\pi \sqrt {\frac{{\text{q}}}{I}} $$

B

$$2\pi \sqrt {{\text{q}}I} $$

C

$$\frac{1}{{2\pi }}\sqrt {\frac{{\text{q}}}{I}} $$

D

$$\frac{1}{{2\pi }}$$

In a gearing system, pump speed is one third of the motor. Shaft from motor is 6 cm in diameter and 30cm long, the impellar shaft is 10cm diameter and 60cm long. Mass moment of inertia is 1500 Kg-m2, C = 80Gn/m2. Neglecting the inertia of shaft and gears calculate the frequency of free torsional vibrations in Hz.

A

4.7

B

5.7

C

4.5

D

5.5

A torsional system with discs of moment of inertia $${I_1}$$ and $${I_2}$$ as shown in the below figure, is gear driven such that the ratio of speed of shaft B to shaft A is 'G'. Neglecting the inertia of gears, the equivalent inertia of disc on shaft B at the speed of shaft A is equal to
Theory of Machine mcq question image

A

$${\text{G}} \times {I_2}$$

B

$${{\text{G}}^2} \times {I_2}$$

C

$$\frac{{{I_2}}}{{\text{G}}}$$

D

$$\frac{{{I_2}}}{{{{\text{G}}^2}}}$$

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

A

1.4

B

0.054

C

0.8

D

1.0

If the mass moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a single motor system?

A

Increases 4 times

B

Increases 2 times

C

Decreases 4 times

D

Decreases 2 times

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$ is equal to = ?

A

24

B

32

C

44

D

100

A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a single node system in Hz if the mass moment of inertia of rotors in Kg-m2 are: 0.15, 0.3 and 0.09. C=84 kN/mm2

A

171

B

181

C

191

D

201

A single cylinder oil engine works with a three rotor system, the shaft length is 2.5m and 70mm in diameter, the middle rotor is at a distance 1.5m from one end. Calculate the free torsional vibration frequency for a two node system in Hz if the mass moment of inertia of rotors in Kg-m2 are: 0.15, 0.3 and 0.09. C=84 kN/mm2

A

257

B

281

C

197

D

277

If the polar moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a single motor system?

A

Increases 4 times

B

Increases 2 times

C

Decreases 4 times

D

Decreases 2 times

In the given figure, considering PN as one shaft, If the mass moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a rotor at P?

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