# Strength of Materials Questions and Answers – Polar Moment of Inertia

This set of Strength of Materials Multiple Choice Questions & Answers (MCQs) focuses on “Polar Moment of Inertia”.

1. The moment of inertia of a plane area with respect to an axis ____________ to the plane is called a polar moment of inertia.
a) Parallel
b) Perpendicular
c) Equal
d) Opposite

Explanation: The moment of inertia of a plane area with respect to an axis perpendicular to the plane of the figure is called a polar moment of inertia with respect to a point, where the axis intersects a plane.

2. What are the units of Polar modulus?
a) mm3
b) mm2
c) mm
d) mm4

Explanation: The ratio of polar moment of inertia (J) to the radius of section(R) is known as polar modulus or torsional section modulus. Its units are mm3.

3. What is the polar modulus for solid shaft?
a) π/16 D2
b) π/12 D3
c) π/ 16 D3
d) π/16 D

Explanation: For solid shaft Z = J/R = π/32 × D4/ D/2.
Z = π/16 D3.

4. Calculate the polar moment of inertia for a solid circular shaft of 30 mm diameter.
a) 76m4
b) 79.5m4
c) 81m4
d) 84m4

Explanation: Diameter of the shaft = 30 mm
Polar moment of inertia = J = π/32 × (30)4 mm4
J = 79.52 m4.

5. 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

Explanation: For hollow circular shaft, outside diameter = 120 mm; d = 120-2×20 = 80 mm
the polar moment of inertia = π/32 × (1204– 804).
J = 16.36 × 106 mm4.

6. Determine the maximum flood discharge from a catchment area of 40.25 km2 and it is situated in the Western Ghats.
a) 350 cumecs
b) 375 cumecs
c) 400 cumecs
d) 425 cumecs

Explanation: Since the catchment area is situated in the Western Ghats, the formula best suited is Dicken’s formula and the coefficient of Dicken’s may be taken as 25.
Q = CA3/4
Q = 25×(40.25)3/4
Q = 400 cumecs.

7. Which of the following is known as “under sluices”?
a) Scouring Sluices
b) Divide wall

Explanation: The openings provided in a body wall of the weir almost at the bed level of the river are known as scouring sluices. These are also known as under sluices.

8. _______ provides straight approach to the scouring sluices.
b) Silt Excluder
c) Divide wall
d) Guide banks

Explanation: A divide wall is a long solid wall constructed perpendicular to the axis of weir. It provides a straight approach to the scouring sluices. By preventing the formation of cross currents, it protects the body wall of weir.

9. __________ is provided for the easy movement of fish from upstream to downstream.
b) Silt excluder
c) Marginal bunds
d) Marginal embankments

Explanation: A passage provided just by the side of a divide wall for the movement of fish from upstream to downstream or vice versa is known as a fish ladder.

10. __________ is used as measuring device.
b) Divide wall
c) Cross regulator
d) Scouring sluices

Explanation: A structure constructed at the head of the canal to regulate the supply of water into the canal is called “Head Regulator”. The functions:
i. It is used as a measuring device.
ii. It controls the entry of silt into the canal.

11. __________ is provided to prevent the river from outflanking the work.
a) Guide banks
b) Marginal bunds
c) Silt excluder
d) Divide wall

Explanation: Guide banks are provided on either side of the diversion head works in alluvial soils for a smooth non -tortuous approach to the diversion head works and prevent the river from outflanking the work.

12. ____________ are provided to protect the land and property with is likely to be submerged.
a) Weir
b) Divide wall
c) Marginal bunds

Explanation: Marginal Bunds or marginal embankments are provided on either bank of the river upstream side of diversion head works in alluvial soils in order to protect the land and property which is likely to be submerged during ponding of water during floods.

13. _________ is provided to reduce the kinetic energy of falling water in weir.
a) Body wall
b) Curtain walls
c) Downstream apron
d) Shutter

Explanation: The downstream apron is a concrete bed which is provided on the downstream side of a weir in order to reduce the kinetic energy of falling water. It should have sufficient thickness to resist uplift pressure.

14. Curtain walls are provided to increase ________
a) Creep depth
b) Creep area
c) Creep length
d) Creep volume

Explanation: Curtain walls are provided under the upstream and downstream apron at the ends. We are provided to increase the length of creep and thereby to reduce exit gradient.

15. Which of the following are also known as upstream and downstream piles?
a) Talus on upstream and downstream
b) Curtain walls on upstream and downstream
c) Solid apron on upstream and downstream
d) Shutters on crest of weir

Explanation: Curtain walls are provided especially under the upstream and downstream aprons at the respective ends. They are also called as upstream and downstream piles. The length of the curtain wall depends on the nature of subsoil.

Sanfoundry Global Education & Learning Series – Strength of Materials.

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