Question

guys please help me to solve this question........​

Answer 1

Question :

Three spheres of equal masses are arranged as shown in the figure. Find the coordinates of the centre of mass the system.

Solution :

❒ Position vector of centre of mass is given by

$\dag\:\underline{\boxed{\bf{\red{\overrightarrow{r}=\dfrac{m_1\overrightarrow{r_1}+m_2\overrightarrow{r_2}+\dots+m_n\overrightarrow{r_n}}{m_1+m_2+\dots+m_n}}}}}$

Where, r₁, r₂, ... , rₙ denotes position vectors of point masses m₁, m₂, ... , mₙ respectively.

Sphere A : (x₁ | y₁) = (0 | 0)

Sphere B : (x₂ | y₂) = (a/2 | 0)

Sphere C : (x₃ | y₃) = (0 | 2a)

Assuming all three spheres as point masses,

❒ x - coordinate of COM :

$\sf:\implies\:x_{cm}=\dfrac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}$

$\sf:\implies\:x_{cm}=\dfrac{M(0)+M(a/2)+M(0)}{M+M+M}$

$\sf:\implies\:x_{cm}=\dfrac{Ma/2}{3M}$

$\bf:\implies\:x_{cm}=\dfrac{a}{6}$

❒ y - coordinate of COM :

$\sf:\implies\:y_{cm}=\dfrac{m_1y_1+m_2y_2+m_3y_3}{m_1+m_2+m_3}$

$\sf:\implies\:y_{cm}=\dfrac{M(0)+M(0)+M(2a)}{M+M+M}$

$\sf:\implies\:y_{cm}=\dfrac{2Ma}{3M}$

$\bf:\implies\:y_{cm}=\dfrac{2a}{3}$

Coordinates of COM :

$:\implies\:\underline{\boxed{\bf{\gray{r_{cm}=\bigg(\dfrac{a}{6}\ ,\ \dfrac{2a}{3}\bigg)}}}}$

Answer 2

Answer:

Frequency is the number of occurrences of a repeating event per unit of time.

bye......

Explanation:

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