NCERT Class 11 Physics Solutions: Chapter 9 – Mechanical Properties of Solid-Part 4

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Question 9.9:

A steel cable with a radius of supports a chairlift at a ski area. If the maximum stress is not to exceed what is the maximum load the cable can support?

Answer:

Radius of the steel cable,

Maximum allowable stress

Maximum stress

∴Maximum force Maximum stress Area of cross-section

Hence, the cable can support the maximum load of

Question 9.10:

A rigid bar of mass is supported symmetrically by three wires each long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.

Answer:

The tension force acting on each wire is the same. Thus, the extension in each case is the same. Since the wires are of the same length, the strain will also be the same. The relation for Young’s modulus is given as:

Where,

Tension force

Area of cross-section

Diameter of the wire

It can be inferred from equation that

Young’s modulus for iron,

Diameter of the iron wire

Young’s modulus for copper,

Diameter of the copper wire

Therefore, the ratio of their diameters is given as:

Question 9.11:

A mass, fastened to the end of a steel wire of unstretched length is whirled in a vertical circle with an angular velocity at the bottom of the circle. The cross-sectional area of the wire is . Calculate the elongation of the wire when the mass is at the lowest point of its path.

Answer:

Mass,

Length of the steel wire,

Angular velocity,

Cross-sectional area of the wire,

Let be the elongation of the wire when the mass is at the lowest point of its path.

When the mass is placed at the position of the vertical circle, the total force on the mass is:

Young’s modulus for steel

Hence, the elongation of the wire is