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## What is the position of centre of gravity of a rectangular lamina?

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Question

## What is the position of centre of gravity of a rectangular lamina?

**A**

## At the mid point of longer side

**B**

## At the mid point of shorter side

**C**

## At the point of intersection of its diagonals

**D**

## At one of the corners

Medium Open in App Solution Verified by Toppr

Correct option is C)

## Centre of gravity means a point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass. Hence for a regular shaped bodies it will have at the centre of that body. Hence for a rectangle it is nothing but at the point of intersection of diagonals.

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## What is the position of the center of gravity of a class 11 physics CBSE

What is the position of the center of gravity of a rectangular lamina A At the midpoint of the longer side B At the midpoint of the shorter side C At the point of intersection of its diagonals D At one

What is the position of the center of gravity of a rectangular lamina?A. At the midpoint of the longer side

B. At the midpoint of the shorter side

C. At the point of intersection of its diagonals

D. At one of the corners

Verified 152.7k+ views

**Hint:**In regular shaped bodies, the center of mass and the center of gravity both are at the same point due to the uniform distribution of masses. In an irregular shaped body, there is a difference in position between the center of mass and the center of gravity. This is because of the irregular distribution of masses over the body.

**Complete answer:**

Centre of gravity is defined as the point from which the weight of the entire body or a system is acting. The center of gravity is the center of mass of the body when the gravity of the place is uniform. The center of a regular shaped body will be the center of gravity of that body.

The center of mass is the mean point of mass in the object while the center of gravity is the point on which gravity seems to act. They are not the same.

Let us take a rectangular lamina ABCD, where point A is situated at the origin of a Cartesian plane.

Now, length of the lamina is taken as 2a and breadth is taken as a.

Assume that the mass of the lamina are equally distributed at four corners and taken as m.

So, the centre of mass due to masses at A and B will be situated at M which is the midpoint of the length 2a. i.e. (a, 0)

And the centre of mass due to masses at C and D will be situated at L which is the midpoint of the length 2a. i.e. (a, a)

Now, find the centre of mass of masses located at L and M using the formula,

x= m x l +m x m m+m = x l + x m 2 y= m y l +m y m m+m = y l + y m 2

x=mxl+mxmm+m=xl+xm2y=myl+mymm+m=yl+ym2

Now, substitute the values for x and y for respective masses and we get,

x= x l + x m 2 = a+a 2 =a y= y l + y m 2 = a+0 2 = a 2

x=xl+xm2=a+a2=ay=yl+ym2=a+02=a2

So, we got the point where centre of mass of the lamina is situated as

(a, a 2 ) (a,a2)

which is same as the point of intersection of diagonals for a rectangle having length 2a and breadth a.

Hence, for a rectangular lamina center of gravity is the point of intersection of the diagonals.

**So, the correct answer is “Option C”.**

**Note:**

Another method for calculating mass element

dm dm

for the calculation of center of gravity of irregular objects are as follows:

First we need to find surface mass density which is nothing but total mass per unit area and then multiplying it by total area.

i.e., σ= M A σ=MA Where, σ σ is mass density.

M and A are total mass and total area of the body respectively.

Then, dM=σdA dM=σdA and dM=σdA dM=σdA .

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## What is the position of the center of gravity of a rectangular lamina?

Answer (1 of 2): Why is the center of gravity of a rectangular lamina? Why is it what? Why is at at the centre? It isn’t unless the lamina is lying flat. If it is hanging by a corner, the centre of gravity is slightly below the centre of mass. That’s because gravity decreases with altitude. Howe...

What is the position of the center of gravity of a rectangular lamina?

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2 Answers Terry Moore

, former Statistics lecturer at Massey University (1978-2000)

Answered 3 years ago · Author has 11.6K answers and 9.7M answer views

Originally Answered: Why is the center of gravity of a rectangular lamina?

Why is the center of gravity of a rectangular lamina?

Why is it what? Why is at at the centre? It isn’t unless the lamina is lying flat. If it is hanging by a corner, the centre of gravity is slightly below the centre of mass. That’s because gravity decreases with altitude. However, the difference is very small. Of course if the lamina is non-uniform, the centre of mass will not be at the centre of area.

Edit: perhaps I should explain how to find the centre of mass. I think Archimedes invented the idea of moments, but his moments were for forces. You want the moments of masses. Take moments abou

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Franco Ligabue

, Research Associate at Scuola Normale Superiore (1991-present)

Answered 4 years ago

if the surface density is uniform and the gravitational field can be considered uniform in the region occupied by the lamina, then the centre of gravity coincides with the centre of mass, which is located at the centre of the rectangle (intersection of the diagonals).

1.3K viewsView upvotes

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Related answers Related Answer Kim Aaron

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What's the difference between the centre of gravity and the centre of mass?

Does the centre of gravity and mass lie on the same point?

No. But the difference is very small. For most practical purposes down here on the ground, or even flying in the air, the difference is irrelevant. But the difference can be quite important for spacecraft, though.

Consider the following very simple spacecraft. The two balls are identical. They each have the same mass. The line connecting them has no mass.

The center of mass is right at the midpoint of that line:

The little BMW symbol is the standard symbol for center of mass.

Now suppose this spacecraft is in orbit around the Earth. I’ve sh

Related Answer Naman Mishra

, lives in Kanpur, Uttar Pradesh, India

Answered 3 years ago

How does the force of gravity vary with the distance to the center of the Earth?

Originally Answered: Does gravity decrease as we go towards the center of earth? If yes then why?

Yes, you are right gravity decreases both when you go above the surface of earth or go deep down from the surface of earth.

We all know the famous formula for claculation of gravitational force

Fg=Gm1m2/r²

According to this formula, as the distance between the two bodies increases, the Gravitational force decreses because they are inversely proportional to each other. Thus, on going higher the gravitational pull weakens.

When move deep into the eath towards its centre the gravity decraces too, WHY??

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Answered Feb 13, 2022 · Author has 330 answers and 330.6K answer views

How can the position of the center of gravity of a semicircle be found?

We know the centre of gravity would lie in the axis of symmetry. For this given semi-circle, the axis of symmetry would be

y=0 y=0

Let the mass of the semi-circle

=M =M

and radius of semi-circle

=r =r . Mass density =λ= 4M π r 2 =λ=4Mπr2

Let the centre of gravity

= x c =xc

The small mass in this small area,

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