Is centre of mass important for JEE?

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Syed Aquib Ur Rahman | Contributor-Level 10

6 months ago

Yes, it's an important concept to tackle JEE Main questions on rotational mechanics, rigid bodies, and collisions. Learning about the centre of mass simplifies complex motions of objects by treating the entire mass into a single point. In exams such as JEE, questions on centre of mass are also inte

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The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position (xa/3π, xa/3π) where x is---------. (Round off to the Nearest integer) [a is an area as shown in the figure]

Alok Kumar Singh

The x and y coordinates of the center of mass are given by:
x? = y? = 4a / 3π

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 $k g$ . (the coordinates of the same are shown in figure) are:



Raj Pandey

$(0,3)$

$\begin{array}{r} {\overset{?}{r}}_{c m} = \frac{1 \times (\frac{\hat{i}}{2} + \hat{j}) + 1 \times (\hat{i} + \frac{5 \hat{j}}{2})}{2} \\ {\overset{?}{r}}_{c m} = \frac{3}{4} \hat{i} + \frac{7}{4} \hat{j} \end{array}$

$(0,0)$

A body of mass 2 kg moving with a speed of 4 m/s, makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is x/10 m/s. Then the value of x is _______ .

Raj Pandey

From conservation of momentum:
2×4 = 2v? + mv?
Given v? = 1 m/s (interpreted from intermediate steps)
8 = 2 (1) + mv?
mv? = 6 . (i)
From coefficient of restitution (e=1 for elastic collision):
e = (v? - v? )/ (u? - u? )
1 = (v? - v? )/ (4 - 0)
-1 = (v? - v? )/ (0 - 4) (as written in the image)
⇒ 4 =

Payal Gupta

$X_{c} = Y_{c} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}} = \frac{m \times 0 + m \times 0 + m \times 3}{3 m} = 1 m$

$O C = X \sqrt[]{x_{0}^{2} + Y_{c}^{2}} = \sqrt[]{{(1)}^{2} + {(1)}^{2}} = \sqrt[]{2} m$

How to find shift in centre of mass?

Syed Aquib Ur Rahman

You should know that when the shift in the centre of mass occurs, you can use the principle of moments. With this logic, we can see the shift from the original body as the combination of two parts. The one that remains part and the other that is removed. The formula for the shift is the product of t