# Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge$ and $ - \mathop i\limits^ \wedge - \mathop j\limits^ \wedge - \mathop k\limits^ \wedge $ respectively would have the center of mass at

A. $ - \dfrac{{\left( {\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge } \right)}}{2}$

B. $\dfrac{{\left( {\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge } \right)}}{2}$

C. $ - \dfrac{{\left( {\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge } \right)}}{4}$

D. $\dfrac{{\left( {\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge } \right)}}{4}$

Answer

Verified

280.2k+ views

**Hint:**The center of mass is a position defined relative to an object or a system of objects. It is the average position of all parts of the given system, weighted according to their masses. There are situations in which the center of mass does not fall anywhere on the object.

**Complete step by step answer:**

Given, Mass of first particle is: ${m_1} = 10\,kg$

And the position vector is $\mathop {{r_1}}\limits^ \to = \mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge $

Mass of second particle is: ${m_2} = 30\,kg$

And the position vector is $\mathop {{r_2}}\limits^ \to = - \mathop i\limits^ \wedge - \mathop j\limits^ \wedge - \mathop k\limits^ \wedge $

$\text{Center of mass}= \dfrac{{{m_1}\mathop {{r_1}}\limits^ \to + {m_2}\mathop {{r_1}}\limits^ \to }}{{{m_1} + {m_2}}}$

$\Rightarrow \text{Center of mass} = \dfrac{{10\left( {\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge } \right) + 30\left( { - \mathop i\limits^ \wedge - \mathop j\limits^ \wedge - \mathop k\limits^ \wedge } \right)}}{{10 + 30}}$

$\therefore \text{Center of mass} = - \left( {\dfrac{{\mathop i\limits^ \wedge + \mathop j\limits^ \wedge + \mathop k\limits^ \wedge }}{2}} \right)$

**Therefore, option A is the correct answer.**

**Note:**The position vectors in physics are straight lines having one end fixed to a body and the other end attached to a moving point. They are used to describe the position of the point relative to the body. As the point moves, the position vector changes in length or in direction or in both length and direction. Note that the center of mass may sometimes lie outside the physical body. This happens in the case of hollow or open shaped objects like horseshoes.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Which of the following would not be a valid reason class 11 biology CBSE

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What is meant by monosporic development of female class 11 biology CBSE

Trending doubts

The ray passing through the of the lens is not deviated class 10 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

What is the nlx method How is it useful class 11 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the difference between anaerobic aerobic respiration class 10 biology CBSE