The torque transmitted by a hollow shaft of outer diameter (D) and inner diameter (d) is

Two shafts A and B are made of the same material. The diameter of shaft A is twice as that of shaft B. The power transmitted by the shaft A will be __________ of shaft B.

A

Twice

B

Four times

C

Eight times

D

Sixteen times

The strain energy stored in a hollow circular shaft of outer diameter (D) and inner diameter (d) subjected to shear stress is

A

$$\frac{{{\tau ^2}}}{{2{\text{C}}}}\left( {\frac{{{{\text{D}}^2} - {{\text{d}}^2}}}{{\text{D}}}} \right) \times {\text{Volume of shaft}}$$

B

$$\frac{{{\tau ^2}}}{{2{\text{C}}}}\left( {\frac{{{{\text{D}}^2} + {{\text{d}}^2}}}{{\text{D}}}} \right) \times {\text{Volume of shaft}}$$

C

$$\frac{{{\tau ^2}}}{{4{\text{C}}}}\left( {\frac{{{{\text{D}}^2} - {{\text{d}}^2}}}{{\text{D}}}} \right) \times {\text{Volume of shaft}}$$

D

$$\frac{{{\tau ^2}}}{{4{\text{C}}}}\left( {\frac{{{{\text{D}}^2} + {{\text{d}}^2}}}{{\text{D}}}} \right) \times {\text{Volume of shaft}}$$

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

A

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

B

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

C

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

D

$$\frac{\pi }{{64}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$

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 will transmit a __________ torque than a solid shaft of the same mass and same material.

A

Smaller

B

Greater

C

Medium

D

None of these

The torque transmitted by a solid shaft of diameter (D) is (where $$\tau $$ = Maximum allowable shear stress)

A

$$\frac{\pi }{4} \times \tau \times {{\text{D}}^3}$$

B

$$\frac{\pi }{{16}} \times \tau \times {{\text{D}}^3}$$

C

$$\frac{\pi }{{32}} \times \tau \times {{\text{D}}^3}$$

D

$$\frac{\pi }{{64}} \times \tau \times {{\text{D}}^3}$$

Two shafts ‘A’ and ‘B’ under pure torsion are of identical length and identical weight and are made of the same material. The shaft ‘A’ is solid and the shaft ‘B’ is hollow. We can say that

A

Shaft B is better than shaft A

B

Shaft A is better than shaft B

C

Both the shafts are equally good

D

None of these

A hollow shaft of same cross-section area as compared to a solid shaft transmit

A

Same torque

B

Less torque

C

More torque

D

Unpredictable

The frictional torque transmitted in a conical pivot bearing, considering uniform pressure, is (where R = Radius of shaft and $$\alpha $$ = Semi-angle of the cone)

A

$$\frac{1}{2}\mu {\text{WRcosec}}\alpha $$

B

$$\frac{2}{3}\mu {\text{WRcosec}}\alpha $$

C

$$\frac{3}{4}\mu {\text{WRcosec}}\alpha $$

D

$$\mu {\text{WRcosec}}\alpha $$

The radius of a friction circle for a shaft rotating inside a bearing is (where r = Radius of shaft and $$\tan \varphi $$ = Coefficient of friction between the shaft and bearing)

A

$${\text{r}}\sin \varphi $$

B

$${\text{r}}\cos \varphi $$

C

$${\text{r}}\tan \varphi $$

D

$$\frac{{\text{r}}}{2}\cos \varphi $$

The torque transmitted by a hollow shaft of outer diameter (D) and inner diameter (d) is

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