Stress And Strain

The correct answer is(D): 1.8×10²N.

For $Cu$ wire, $l_%7B1%7D%3D2.2%20%5C%2Cm$ ,
$r_%7B1%7D%3D1.5%20%5C%2Cmm%20%3D1.5%20%5Ctimes%2010%5E%7B-3%7D%20m$
$Y_%7B1%7D%3D1.1%20%5Ctimes%2010%5E%7B11%7D%20%5C%2CN%20%2F%20m%20%5E%7B2%7D$
For steel wire, $l_%7B2%7D%3D1.6%5C%2Cm$ ,
$r_%7B2%7D%3D1.5%20%5C%2C%20mm%20%3D1.5%20%5Ctimes%2010%5E%7B-3%7D%20m$
$Y_%7B2%7D%3D2.0%20%5Ctimes%2010%5E%7B11%7D%20%5C%2C%20N%20%2F%20m%20%5E%7B2%7D$
Let $F$ be the stretching force in both the wires then
For $Cu$ wire, $Y_%7B1%7D%3D%5Cfrac%7BF%7D%7B%5Cpi%20r_%7B1%7D%5E%7B2%7D%7D%20%5Ctimes%20%5Cfrac%7Bl_%7B1%7D%7D%7B%5CDelta%20l_%7B1%7D%7D$
$%5CRightarrow%20F%3D%5Cfrac%7BY_%7B1%7D%20%5Cpi%20r_%7B1%7D%5E%7B2%7D%20%5Ctimes%20%5CDelta%20l_%7B1%7D%7D%7Bl_%7B1%7D%7D$
$%3D%5Cfrac%7B1.1%20%5Ctimes%2010%5E%7B11%7D%7D%7B2.2%7D%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%5Cleft(1.5%20%5Ctimes%2010%5E%7B-3%7D%5Cright)%5E%7B2%7D%20%5Ctimes%200.5%20%5Ctimes%2010%5E%7B-3%7D$
$%5Ccong%201.8%20%5Ctimes%2010%5E%7B2%7D%20N$

The total energy

E

of a satellite in a circular orbit is given by the sum of its kinetic and potential energy. The kinetic energy

K

is:

K%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20m%20v%5E2

where

v

is the orbital velocity of the satellite. The potential energy

U

is given by:

U%20%3D%20-%20%5Cfrac%7BG%20m%20M%7D%7BR%20%2B%20h%7D

where

G

is the gravitational constant,

m

is the mass of the satellite,

M

is the mass of the Earth, and

R%20%2B%20h

is the distance from the center of the Earth to the satellite. Using the fact that the orbital velocity

v

of a satellite is:

v%20%3D%20%5Csqrt%7B%5Cfrac%7BGM%7D%7BR%20%2B%20h%7D%7D

we can substitute this into the kinetic energy equation:

K%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20m%20%5Cleft(%20%5Cfrac%7BGM%7D%7BR%20%2B%20h%7D%20%5Cright)

Thus, the total energy

E

is:

E%20%3D%20K%20%2B%20U%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20m%20%5Cleft(%20%5Cfrac%7BGM%7D%7BR%20%2B%20h%7D%20%5Cright)%20-%20%5Cfrac%7BG%20m%20M%7D%7BR%20%2B%20h%7D%20%3D%20-%20%5Cfrac%7BG%20m%20M%7D%7B2%20(R%20%2B%20h)%7D

This shows that the total energy

E

is inversely proportional to

(R%20%2B%20h)%5E2

. Therefore, the correct answer is:

%5Cfrac%7B1%7D%7B(R%20%2B%20h)%5E2%7D

About Stress And Strain - KCET

Stress And Strain is a vital chapter for KCET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Stress And Strain PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Stress And Strain carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
3 MCQs

Official Solution

Official Solution

Official Solution

About Stress And Strain - KCET

Frequently Asked Questions

Why focus on Stress And Strain PYQs?

How to best use this analysis?

Stress And Strain

High-Yield Trend

Chapter Questions 3 MCQs

Official Solution

Official Solution

Official Solution

About Stress And Strain - KCET

Frequently Asked Questions

Why focus on Stress And Strain PYQs?

How to best use this analysis?

Chapter Questions
3 MCQs