Question

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Answer 1

Question:

• Three rods of the same mass are placed as shown in the figure. What will be the Coordinate of centre of mass of the system ?

Answer:

$\large\bold\red{(d)\;(\frac{a}{3},\frac{a}{3})}$

Explanation:

Given,

• Three rods of same mass are placed to form a right angled triangle in Cartesian plane.

Note:- Refer to the attachment for Diagram.

Now,

We know that,

• Centre of mass of each rod will be at it's mid point of length.

Therefore,

• Coordinates of their COM will be at $\bold{(\frac{a}{2}, 0),(0, \frac{a}{2} )\;and\;( \frac{a}{2} , \frac{a}{2} )}$ for rods at X axis, Y axis and hypotenus of the triangle respectively.

Therefore,

Now,

For the whole system,

$= > x_{CM} = \frac{m( \frac{a}{2}) + m(0) + m( \frac{a}{2} )}{m + m + m} \\ \\ = > x_{CM} = \cancel\frac{am }{3m} \\ \\ = > x_{CM} = \frac{a}{3}$

Similarly,

We get,

$= > y_{CM} = \frac{ m(0) + m( \frac{a}{2}) + m( \frac{a}{2} )}{m + m + m} \\ \\ = > y_{CM} = \cancel\frac{am }{3m} \\ \\ = > y_{CM} = \frac{a}{3}$

Thus,

• The Coordinate of COM for the system is, $\bold{(\frac{a}{3},\frac{a}{3})}$.

Hence,

Option (d) is Correct answer.

Answer 2

Answer:

Learn from the attachment

Hope this helps you