Question

5. Three masses 3,4 and 5 kg are located at the corners of an equilateral triangle of side 1m. La
centres of mass of the system.​

Answer 1

Explanation:

Physics is the natural science that studies matter, its motion and behavior through space and time, and the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

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Answer 2

$\large{\red{\frak{ Given}}}\begin{cases}\textsf{ Three masses of 3kg , 4 kg and 5kg are on the corners of the triangle. }\\\textsf{ The side of the equilateral triangle is 1m. }\end{cases}$

$\large{\red{\frak{ To \ Find }}}\begin{cases}\textsf{The coordinates of the centre of mass .}\end{cases}$

Here we need to find the coordinates of the centre of mass of the system . There are masses of 3kg , 4kg and 5kg at the corners of the triangle and the side of the triangle is 1m .

So lets make a graph of the system, where one of the vertex of the triangle is at the origin that is (0,0) . And hence the second coordinate is (1,0 ). The coordinates of the midpoint of this line will be (0.5,0) . Let's find out the coordinates of the third coordinate of triangle using the Pythagoras Theorem. For its steps kindly refer to the attachment. Hence we see that the ,

$\sf:\implies\boxed{ \green{\sf Third \ Coordinate \ = \ \bigg(\dfrac{1}{2},\dfrac{\sqrt3}{2}\bigg) }}$

$\purple{\bigstar}\underline{\boldsymbol{ According\ to\ the \ Question :-}}$

$\sf:\implies \pink{ ( x , y )=\bigg( \dfrac{mx_1 + mx_2+mx_3}{m_1+m_2+m_3} , \dfrac{my_1 + my_2+my_3}{m_1+m_2+m_3} \bigg) }\\\\\sf:\implies (x,y)= \bigg( \dfrac{ (3)(0)+(4)(1)+(5)(0.5)}{3+4+5},\dfrac{(3)(0)+(4)(0)+(5)\bigg(\dfrac{\sqrt3}{2}\bigg) }{3+4+5}\bigg)\\\\\sf:\implies (x,y)=\bigg( \dfrac{6.5}{12},\dfrac{5\sqrt3}{24}\bigg)\\\\\sf:\implies\underset{\blue{\sf Required\ coordinate }}{\underbrace{ \boxed{\pink{\frak {(x,y)= (0.54,0.36)}}}}}$