# NCERT Class 11 Physics Solutions: Chapter 9 – Mechanical Properties of Solid-Part 8

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**Question 9.19:**

A mild steel wire of length and cross-sectional area is stretched, well within its elastic limit, horizontally between two pillars. A mass of is suspended from the mid-point of the wire. Calculate the depression at the mid-point.

**Answer:**

Length of the steel wire

Area of cross-section,

A mass is suspended from its midpoint.

Hence, the wire dips, as shown in the given figure.

Original length

Depression

The length after mass m, is attached to the wire

Increase in the length of the wire:

Where,

Expanding and neglecting higher terms, we get:

Let be the tension in the wire.

Using the figure, it can be written as:

Expanding the expression and eliminating the higher terms:

Young’s modulus of steel,

Hence, the depression at the midpoint is

**Question 9.20:**

Two strips of metal are riveted together at their ends by four rivets, each of diameter . What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed ? Assume that each rivet is to carry one quarter of the load.

**Answer:**

Diameter of the metal strip,

Maximum shearing stress

Maximum force Maximum stress Area

Each rivet carries one quarter of the load.

∴ Maximum tension on each rivet

**Question 9.21:**

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of water. The water pressure at the bottom of the trench is about . A steel ball of initial volume is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?

**Answer:**

Water pressure at the bottom,

Initial volume of the steel ball,

Bulk modulus of steel,

The ball falls at the bottom of the Pacific Ocean, which is beneath the surface.

Let the change in the volume of the ball on reaching the bottom of the trench be

Bulk modulus,

Therefore, the change in volume of the ball on reaching the bottom of the trench is .