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

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

Bissoy MCQ
#Mechanical Engineering #Strength Of Materials In ME

Related Questions

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 $$\frac{\pi }{{32}}\left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$
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 torque transmitted by a hollow shaft of outer diameter (D) and inner diameter (d) is
A $$\frac{\pi }{4} \times \tau \left( {\frac{{{{\text{D}}^2} - {{\text{d}}^2}}}{{\text{D}}}} \right)$$
B $$\frac{\pi }{{16}} \times \tau \left( {\frac{{{{\text{D}}^3} - {{\text{d}}^3}}}{{\text{D}}}} \right)$$
C $$\frac{\pi }{{16}} \times \tau \left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$
D $$\frac{\pi }{{32}} \times \tau \left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$
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 $$\frac{1}{{2\pi }}$$
The polar moment of inertia of a solid circular shaft of diameter (D) is
A $$\frac{{\pi {{\text{D}}^3}}}{{16}}$$
B $$\frac{{\pi {{\text{D}}^3}}}{{32}}$$
C $$\frac{{\pi {{\text{D}}^4}}}{{32}}$$
D $$\frac{{\pi {{\text{D}}^4}}}{{64}}$$
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
In order to have a connecting rod equally strong in buckling about X-axis and Y-axis, the moment of inertia about X-axis should be __________ the moment of inertia about Y-axis.
A Equal to
B Twice
C Three times
D Four times
Mass moment of inertia of a thin rod about its one end is ___________ the mass moment of inertia of the same rod about its mid-point
A Same as
B Twice
C Thrice
D Four times
The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is
A $$\frac{1}{4}$$
B $$\frac{1}{2}$$
C $$\frac{3}{4}$$
D $$2$$
When a shaft is subjected to combined twisting moment (T) and bending moment (M), then the equivalent twisting moment is equal to
A $$\frac{1}{2}\sqrt {{{\text{M}}^2} + {{\text{T}}^2}} $$
B $$\sqrt {{{\text{M}}^2} + {{\text{T}}^2}} $$
C $$\frac{1}{2}\left( {{\text{M}} + \sqrt {{{\text{M}}^2} + {{\text{T}}^2}} } \right)$$
D $${\text{M}} + \sqrt {{{\text{M}}^2} + {{\text{T}}^2}} $$

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