Mechanical Properties of Solids Test - 5

Because, the stretching of coil simply changes its shape without any change in the length of the wire used in coil. Due to which shear modulus of elasticity is involved.

Elasticity is a measure of tendency of the body to regain its original configuration. As steel is deformed less than rubber therefore steel is more elastic than rubber.

Let us consider the shaft as a cylinder. Then we have a solid cylinder A with radius D and a hollow cylinder B with inner radius d and outer radius D as shown in the figure.

If both the cylinders are made of the same material, clearly the mass of the A is greater than the mass of B as cylinder B is hollow.

Now if we assume that both the cylinders are made of the same mass, then the cylinder B is stronger than the cylinder A as the mass in the centre of cylinder B is spread at a smaller area.

Thus we can say that a hollow shaft is found to be stronger than a solid shaft made of the same size and material or that the assertion is true.

If the force is applied on the external diameter of both the cylinders, then the distance where the force is applied will remain constant. But we saw that the cylinder B is stronger than the cylinder A then we can say that cylinder B needs more force and hence more torque as compared to the cylinder A.

Then, the reason is also correct.

Hence, the answer is A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

Strain is the ratio of change in dimensions of the body to the original dimensions. Because this is a ratio, therefore it is dimensionless quantity.

Ivory is more elastic than wet-clay. Hence the ball of ivory will rise to a greater height. In fact the ball of wet-clay will not rise at all, it will be somewhat flattened permanently.

Work done = 1/2 × Stress × Strain = 1/2 × Y × (Strain)² Since, elasticity of steel is more than copper, hence more work has to be done in order to stretch the steel.

When a spring balance has been used for a long time, the spring in the balance fatigued and there is loss of strength of the spring. In such a case, the extension in the spring is more for a given load and hence the balance gives wrong readings.

In a glassy solid (i.e., amorphous solid) the various bonds between the atoms or ions or molecules of a solid are not equally strong. Different bonds are broken at different temperatures. Hence there is no sharp melting point for a glassy solid.

Bulk modulus of elasticity measures how good the body is to regain its original volume on being compressed. Therefore, it represents incompressibility of the material. K = -PV/ΔV where P is increase in pressure, ΔV is change in volume.

A bridge during its use undergoes alternating strains for a large number of times each day, depending upon the movement of vehicles on it when a bridge is used for long time, it losses its elastic strength. Due to which the amount of strain in the bridge for a given stress will become large and ultimately, the bridge may collapse. This may not happen, if the bridges are declared unsafe after long use.

Young's Modulus= (restoring force per unit area)/(elongation of wire/length of wire) now for a plastic body the restoring force is zero and it ultimately makes the Young's modulus zero. Hence both assertion and reason are true

Stress is defined as internal force (restoring force) per unit area of a body. Also, rubber is less elastic than steel, because restoring force is less for rubber than steel.