The polar moment of inertia of a hollow shaft of outer diameter (D) and inner diameter (d) is

Two shafts 'A' and 'B' are made of same material. The shaft 'A' is solid and has diameter D. The shaft 'B' is hollow with outer diameter D and inner diameter $$\frac{{\text{D}}}{2}$$. The strength of hollow shaft in torsion is _________ as that of solid shaft.

A

$$\frac{1}{{16}}$$

B

$$\frac{1}{8}$$

C

$$\frac{1}{4}$$

D

$$\frac{{15}}{{16}}$$

Two shafts 'A' and 'B' have the same material. The shaft 'A' is solid of diameter 100 mm. The shaft 'B' is hollow with outer diameter 100 mm and inner diameter 50 mm. The torque transmitted by shaft 'B' is __________ as that of shaft 'A'.

A

$$\frac{1}{6}$$

B

$$\frac{1}{8}$$

C

$$\frac{1}{4}$$

D

$$\frac{{15}}{{16}}$$

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

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

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

The polar modulus for a hollow shaft of outer diameter (D) and inner diameter (d) is

A

$$\frac{\pi }{4}\left( {\frac{{{{\text{D}}^2} - {{\text{d}}^2}}}{{\text{D}}}} \right)$$

B

$$\frac{\pi }{{16}}\left( {\frac{{{{\text{D}}^3} - {{\text{d}}^3}}}{{\text{D}}}} \right)$$

C

$$\frac{\pi }{{16}}\left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$

D

$$\frac{\pi }{{32}}\left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$

A hollow shaft has outside diameter 120 mm and thickness 20 mm. Find the polar moment of inertia (J).

A

16.36 × 106 mm4

B

14.65 × 106 mm4

C

10.32 × 106 mm4

D

23.18 × 106 mm4

A hollow shaft outside diameter 120 mm and thickness 20 mm. Find polar moment of inertia.

A

16.36 × 106 mm4

B

18.45 × 106 mm4

C

21.3 × 106 mm4

D

22.5 × 106 mm4

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.
Classical Mechanics mcq question image

The moment of inertia of the resulting body about Y-axis is

A

$$\frac{{\pi \rho {R^5}}}{4}$$

B

$$\frac{{5\pi \rho {R^5}}}{{12}}$$

C

$$\frac{{7\pi \rho {R^5}}}{{12}}$$

D

$$\frac{{3\pi \rho {R^5}}}{4}$$

A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the radial stress due to shrink shift in inner tube. b) -3.04 c) -3.04 d) +3.04

A

+3.04

B

1-(15/r) ²

C

1-(15/r) ²

D

1-(15/r) ²

A high pressure cylinder consists of a steel tube with inner and outer diameters 30 and 60mm respectively. It is jacketed by an outer steel tube, having an outer diameter of 90mm. Maximum principal stress induced is 80N/mm². Calculate the tangential stress due to shrink shift in inner tube. b) -3.04 c) -3.04 d) +3.04

A

+3.04

B

1+ (15/r) ²

C

1+ (15/r) ²

D

1+ (15/r) ²

The polar moment of inertia of a hollow shaft of outer diameter (D) and inner diameter (d) is

Related Questions