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Mechanical Properties Of Solids

The stress-strain graphs for materials A and B are shown in Fig. 9.12.

The graphs are drawn to the same scale.

(a) Which of the materials has the greater Young’s modulus?

(b) Which of the two is the stronger material?

Mechanical Properties Of Solids

Figure 9.11 shows the strain-stress curve for a given material.

What are (a) Young’s modulus and

(b) approximate yield strength for this material?

Mechanical Properties Of Solids

A steel wire of length 4.7 m and cross-sectional area 3.0 × 10-5 m² stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–⁵ m² under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Gravitation

A 400 kg satellite is in a circular orbit of radius 2RE about the Earth. How much

energy is required to transfer it to a circular orbit of radius 4RE ? What are the changes in the kinetic and potential energies ?

Gravitation

Express the constant k of Eq.(7.38) in days and kilometres. Given k = 10–13 s²m–3. The moon is at a distance of 3.84 × 10⁵ km from the earth. Obtain its time-period of revolution in days.

Gravitation

Weighing the Earth : You are given the following data: g = 9.81 ms–2,RE = 6.37×10⁶m, the distance to the moon R = 3.84×10⁸m and the time period of the moon’s revolution is 27.3 days. Obtain themass of the Earth ME in two different ways.

Gravitation

The planet Mars has two

moons, phobos and delmos. (i) phobos has

a period 7 hours, 39 minutes and an orbital

radius of 9.4 ×10³km. Calculate the mass

of mars. (ii) Assume that earth and mars

move in circular orbits around the sun,

with the martian orbit being 1.52 times

the orbital radius of the earth. What is

the length of the martian year in days ?

Gravitation

Two uniform solid spheres

of equal radii R, but mass M and 4 M have

a centre to centre separation 6 R, as shown

in Fig. 7.10. The two spheres are held fixed.

A projectile of mass m is projected from the

surface of the sphere of mass M directly

towards the centre of the second sphere.

Obtain an expression for the minimum

speed v of the projectile so that it reaches

the surface of the second sphere.

Gravitation

Find the potential energy of

a system of four particles placed at the

vertices of a square of side l. Also obtain

the potential at the centre of the square.

Gravitation

Three equal masses of m kg

each are fixed at the vertices of an

equilateral triangle ABC.

(a) What is the force acting on a mass 2m

placed at the centroid G of the triangle?

(b) What is the force if the mass at the

vertex A is doubled ?

 Take AG = BG = CG = 1 m (see Fig. 7.5)