Centre of gravity shifted to what position?

[Benjamin_harsh]

Homework Statement

A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of gravity of the remaining portion of the sheet?

Relevant Equations

original side of the square = $2x$

A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of gravity of the remaining portion of the sheet?

a) center of gravity lies at a distance of 5/12 of the side of the original square from each uncut side.
b) center of gravity lies at a distance 7/12 of the side of the original square from each uncut side.
c) center of gravity lies at a distance of 63/4 of the side of the original square from each uncut side.
d) None of these.

Solution:

$\overline X = \large \frac{A_{1}\overline{x_{1}} - A_{1}\overline{x_{2}}}{A_{1}-A_{2}} = \frac{(4x^{2}).(x) - (x^{2})(1.5x)}{4x^{2}-x^{2}}$

$\overline X = \large\frac{5x}{6} = \frac{5}{12}\normalsize(2x)$$\overline Y = \large\frac{A_{1}\overline{y_{1}} - A_{1}\overline{y_{2}}}{A_{1}-A_{2}} = \frac{5x}{6} = \frac{5}{12}\normalsize(2x)$

original side of the square = $2x$

Why they didn't continue after this step: $\frac{5}{12}(2x)$?

 

[mjc123]

Sorry, your solution is unreadable.

 

[Benjamin_harsh]

Sorry, your solution is unreadable.

Now I edited clearly. Please see it.

 

[mjc123]

You have two steps that end with 5/12(2x). Which is the one that "they" didn't continue after? What continuation do you think is necessary? You have the information to answer the question.

 

[Benjamin_harsh]

You have the information to answer the question.

Answer is: center of gravity lies at a distance of $\frac{5}{12}$ of the side of the original square from each uncut side.

Can you show center of gravity before and after cut by drawing the diagram?

 

[mjc123]

A is original CG, B the CG after cut.

 

[Benjamin_harsh]

I am confused at this sentence: $\frac{5}{12}$ of the side of the original square from each uncut side.

How to understand it?

 

[jbriggs444]

I am confused at this sentence: $\frac{5}{12}$ of the side of the original square from each uncut side.

How to understand it?

5/12 of the way from the left (uncut) side toward the right (cut) side.
5/12 of the way from the bottom (uncut) side toward the top (cut) side.

 

[HallsofIvy]

Problem Statement: A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of gravity of the remaining portion of the sheet?
Relevant Equations: original side of the square = $2x$

A square sheet of metal has a square of one quarter of the original area cut from one corner as shown in the figure. Which of the following statements is true about the position of the centre of gravity of the remaining portion of the sheet?

View attachment 245727

a) center of gravity lies at a distance of 5/12 of the side of the original square from each uncut side.
b) center of gravity lies at a distance 7/12 of the side of the original square from each uncut side.
c) center of gravity lies at a distance of 63/4 of the side of the original square from each uncut side.
d) None of these.

Solution:

View attachment 245729

$\overline X = \large \frac{A_{1}\overline{x_{1}} - A_{1}\overline{x_{2}}}{A_{1}-A_{2}} = \frac{(4x^{2}).(x) - (x^{2})(1.5x)}{4x^{2}-x^{2}}$

$\overline X = \large\frac{5x}{6} = \frac{5}{12}\normalsize(2x)$$\overline Y = \large\frac{A_{1}\overline{y_{1}} - A_{1}\overline{y_{2}}}{A_{1}-A_{2}} = \frac{5x}{6} = \frac{5}{12}\normalsize(2x)$

original side of the square = $2x$

Why they didn't continue after this step: $\frac{5}{12}(2x)$?

The question asked was "which of these is correct:
a) center of gravity lies at a distance of 5/12 of the side of the original square from each uncut side.
b) center of gravity lies at a distance 7/12 of the side of the original square from each uncut side.
c) center of gravity lies at a distance of 63/4 of the side of the original square from each uncut side.
d) None of these.
By writing the coordinates of the center of gravity as "(5/12)2x" they thought it was not necessary to say that "a" is correct.