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DC Pandey Solutions: Elasticity | Physics Class 11 - NEET PDF Download

Introductory Exercise 12.1

Ques 1: Two wires A and B of same dimensions are stretched by same amount of force. Young's modulus of A is twice that of B. Which wire will get more elongation?
Sol:
 DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET as Young's modulus of A is twice of B, so elongation of A will be half of B.

Ques 2: A rod 100 cm long and of 2 cm × 2 cm cross-sect ion is subjected to a pull of 1000 kg force. If the modulus of elasticity of the material is 2.0 × 106 kg/cm2, determine the elongation of the rod.
Sol:

 DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

Ques 3: A cast iron column has internal diameter of 200 mm. What should be the minimum external diameter so that it may carry a load of 1.6 MN without the stress exceeding 90 N/mm2?
Sol:
 DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
= 0250 = 250 mm

EXERCISES
For JEE Main

Subjective Questions
Ques 1: A cylindrical steel wire of 3 m length is to stretch no more than 0.2 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?
Ysteel =2.1 × 1011 N/m2
Sol: 

DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
= 1.9 × 10-3 m = 1.9 mm

Ques 2: The elastic limit of a steel cable is 3.0 × 108 N/m2 and the cross-section area is 4cm2. Find the maximum upward acceleration that can be given to a 900 kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.
Sol: 
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

Ques 3: If the elastic limit of copper is 1.5 x 108N/m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg, if its elastic limit is not to be exceeded.
Sol:

 DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

Ques 4: Find the increment in the length of a steel wire of length 5 m and radius 6 mm under its own weight. Density of steel = 8000 kg/m3 and Young's modulus of steel = 2 x 1011 N/m2. What is the energy stored in the wire? (Take g = 9.8m/s2)
Sol:
 DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
= 49 × 10-6 m

Ques 5: Two wires shown in figure are made of the same material which has a breaking stress of 8 × 108 N/m2. The area of cross-section of the upper wire is 0.006 cm2 and that of the lower wire is 0.003 cm . The mass m1 = 10 kg, m2 = 20 kg and the hanger is light. Find the maximum load that can be put on the hanger without breaking a wire. Which wire will break first if the load is increased? (Take g = 10 m/s2)
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
Sol: 
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
= 48 - 30 = 18 kg
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
So, lower wire will break if m > 14 kg. i.e., maximum load which can be put on hanger without breaking wire is 14 kg.

Ques 6: A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of:
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
(a) the stresses developed in the two wires,
(b) the strains developed. (Y of steel =2 × 1011 N/m2 and T of copper = 1.3 × 1011 N/m2)
Sol: 
F/A is same as both have same cross-section area and subjected under same tension.
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

Ques 7: Calculate the approximate change in density of water in a lake at a depth of 400 m below the surface. The density of water at the surface is 1030 kg/m3 and bulk modulus of water is 2 × 109N/m2.
Sol:

 DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

Ques 8: A wire of length 3 m, diameter 0.4 mm and Young's modulus 8 × 1010 N/m2 is suspended from a point and supports a heavy cylinder of volume 10-3 m3 at its lower end. Find the decrease in length when the metal cylinder is immersed in a liquid of density 800 kg/m3.
Sol: 

DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
= -2.39 × 10-3 m

Ques 9: In taking a solid ball of rubber from the surface to the bottom of a lake of 180 m depth, reduction in the volume of the ball is 0.1%. The density of water of the lake is 1 × 103 kg/m . Determine the value of the bulk modulus of elasticity of rubber. (g = 9.8m/s2)
Sol: 
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
= 1.76 × 109 N/m2 

Ques 10: A sphere of radius 10 cm and mass 25 kg is attached to the lower end of a steel wire of length 5 m and diameter 4 mm which is suspended from the ceiling of a room. The point of support is 521 cm above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest position. (Ysteel =2 × 1011 N/m2)
Sol: DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

DC Pandey Solutions: Elasticity | Physics Class 11 - NEET
DC Pandey Solutions: Elasticity | Physics Class 11 - NEET

The document DC Pandey Solutions: Elasticity | Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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FAQs on DC Pandey Solutions: Elasticity - Physics Class 11 - NEET

1. What is elasticity and why is it important in physics?
Ans. Elasticity is a property of materials that describes their ability to deform and return to their original shape when a force is applied and removed. It is important in physics because it helps us understand how materials respond to external forces, such as stress and strain. By studying elasticity, we can determine the strength, flexibility, and stability of different materials.
2. How is elasticity measured and what are its units?
Ans. Elasticity is typically measured using the concept of Young's modulus, which is defined as the ratio of stress to strain. Stress is the force applied per unit area, while strain is the measure of deformation caused by stress. The units of Young's modulus are the same as the units of stress, which is typically measured in pascals (Pa) or newtons per square meter (N/m²).
3. What are some real-life applications of elasticity?
Ans. Elasticity has several practical applications in our daily lives. One common application is in the design of springs, such as those used in mattresses and car suspensions. Elasticity is also important in the construction industry for designing buildings and bridges that can withstand external forces like wind and earthquakes. Additionally, elasticity plays a role in medical devices, such as prosthetics and orthopedic implants, where materials with specific elastic properties are used to mimic natural tissues.
4. How does temperature affect the elasticity of materials?
Ans. Temperature can significantly impact the elasticity of materials. In general, as the temperature increases, the elasticity of most materials decreases. This is because higher temperatures cause the atoms or molecules in a material to vibrate more rapidly, which disrupts the material's internal structure and reduces its ability to return to its original shape. However, some materials, like rubber, exhibit a unique behavior known as "thermal elasticity," where their elasticity actually increases with temperature.
5. Can elasticity be permanent?
Ans. Elasticity is a temporary property of materials, meaning that it is reversible and the material can return to its original shape after the applied force is removed. However, if the applied force exceeds the material's elastic limit, it may undergo permanent deformation or even fracture. In such cases, the material loses its elasticity and cannot return to its original shape. This is why it is important to understand the elastic limits of different materials to prevent damage or failure in various applications.
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