2021 A/L Physics Past Paper · Question 24 (English Medium)

Answer: (2) $B$

What the question asks

Find the point, among $A$ to $E$, where the centre of gravity of the plate is most likely to be.

Relevant theory

The centre of gravity of a body is the point at which the resultant force of gravity or weight of the body acts.

Applying it to this question

The objects in the figure:

The plate $PQRST$ with a square grid.

A string, with the plate hung from $X$ in figure (1) and from $Y$ in figure (2).

In figure (2), the points $A$, $B$, $C$, $D$, $E$ on the vertical line through $Y$.

Only two forces act on the plate.

The pull of the string acts at the point where it is fixed.

The weight acts at the centre of gravity.

The plate is at rest, so the two forces are equal and opposite, on the same vertical line.

Reasoning and calculation

What we read from the figure:

In figure (1), the vertical line from $X$ goes down through the plate.

In figure (2), the vertical line through $Y$ goes down through the plate.

The rule that applies:

The centre of gravity is on the vertical line through the point of hanging.

So it is on both vertical lines. It is where they cross.

Mark the vertical line from $X$ on the plate. Follow the lines of the grid.

It starts near the middle of $ST$ and goes straight down.

Now draw the same line on the plate in figure (2).

It meets the vertical line through $Y$ at the second point below $Y$.

The points $Y$, $A$, $B$, $C$, $D$, $E$ are equally spaced.

So the crossing is $B$.

Reading the options

The second point below $Y$ is $B$.

Only at $B$ is the centre of gravity on both vertical lines.

Option (2).

Why the other options fail

$A$ is on the line through $Y$, but not where the line from $X$ crosses it.

$C$ is the middle of the plate by eye, not the crossing of the two lines.

$D$ is on the line through $Y$, but not on the line from $X$.

$E$ is on the line through $Y$, but not on the line from $X$.

Checks

Does it make sense?

The centre of gravity of a plate lies inside it.

$B$ is inside the plate, between $Y$ and the lower edge.

Each of $A$ to $E$ lies on the line through $Y$, so only one point can also lie on the line from $X$.

Conclusion

The centre of gravity is where the vertical line from $X$ meets the vertical line through $Y$.

That point is $B$. The answer is (2).

A hanging body is at rest only when its centre of gravity is straight below the point of hanging.

Hang it from two points and draw both vertical lines. The centre of gravity is where they cross.

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