# NCERT Physics Class 11 Exemplar Ch 9 Mechanical Properties of Solids Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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## 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