# NCERT Physics Class 11 Exemplar Ch 9 Mechanical Properties of Solids Part 4

## One and More Than One Answer

Q. 21 To what depth must a rubber ball be taken in deep sea so that its volume is decreased by (The bulk modulus of rubber is ; and the density of sea water is

Q.22 A truck is pulling a car out of a ditch by means of a steel cable that is long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is . How much has the cable stretched? (Young’s modulus for steel is

Answer: Let the increase in length be , then

Q.23 Two identical solid balls, one of ivory and the other of wet-clay, are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why?

Answer: As the ivory ball is more elastic than the wet-clay ball, it will tend to retain its shape instantaneously after the collision. Hence, there will be a large energy and momentum transfer compared to the wet clay ball. Thus, the ivory ball will rise higher after the collision.

## Long Question

Q. 24 Consider a long steel bar under a tensile stress due to forces acting at the edges along the length of the bar (Fig. 9.5). Consider a plane making an angle θ with the length. What are the tensile and shearing stresses on this plane?

(a) For what angle is the tensile stress a maximum?

(b) For what angle is the shearing stress a maximum?

Answer: Let the cross-sectional area of the bar be A. Consider the equilibrium of the plane aa′. A force must be acting on this plane making an angle with the normal ON. Resolving F into components, along the plane and normal to the plane

Let the area of the face aa’ be A’, then

The tensile stress and the shearing stress Maximum tensile stress is when and maximum shearing stress when or