Find the Center of Mass of a Thin Plate of Constant

question 221

Multiple Choice

Find the center of mass of a thin plate of constant density covering the given region.
-The region between the $x$ -axis and the curve $y = 5 \csc ^ { 2 } x , \frac { \pi } { 4 } \leq x \leq \frac { 3 \pi } { 4 }$

• A) \(\bar { x } = \frac { 3 \pi } { 8 } , \bar { y } = \frac { 20 } { 3 }\)
• B) \(\bar { x } = \frac { \pi } { 2 } , \bar { y } = \frac { 15 } { 2 }\)
• C) \(\bar { x } = \frac { \pi } { 2 } , \bar { y } = 5\)
• D) \(\bar { x } = \frac { \pi } { 2 } , \bar { y } = \frac { 10 } { 3 }\)

---

Definitions:

Expenses Grouping

The practice of categorizing costs and expenses into distinct groups to simplify financial analysis and reporting.

Organisation Functions

The primary activities and responsibilities that are crucial for the successful operation of a business or organization.

Goal Congruence

The alignment of individual objectives with the overall objectives of the organization to ensure that all members are working towards the same targets.

Decentralised Organisation

An organizational structure where decision-making power is distributed throughout various levels and departments rather than being centralized at the top.