Two bodies of mass 1 kg have position vectors, $bold i with bold hat on top bold space bold plus bold space 2 bold j with bold hat on top bold space bold plus bold k with bold hat on top bold space bold and bold space bold minus 3 bold i with bold hat on top bold space bold minus 2 bold j with bold hat on top bold space bold plus bold k with bold hat on top$ respectively.The centre of mass of this system has a position vector

$negative 2 bold i with hat on top space plus 2 space bold k with hat on top$
$negative 2 bold i with bold hat on top minus bold j with bold hat on top space plus bold k with hat on top$
$2 bold i with bold hat on top minus bold j with bold hat on top space minus bold k with hat on top$
$negative bold i with bold hat on top plus bold j with bold hat on top space plus bold k with hat on top$

Solution

negative 2 bold i with bold hat on top minus bold j with bold hat on top space plus bold k with hat on top

The position vector of centre of mass

$straight r with rightwards arrow on top space equals space fraction numerator straight m subscript 1 stack bold r subscript bold 1 with bold rightwards arrow on top space plus straight m subscript 2 stack bold r subscript blank subscript bold 2 end subscript with bold rightwards arrow on top over denominator straight m subscript 1 plus straight m subscript 2 end fraction equals space fraction numerator 1 space left parenthesis straight i with hat on top plus 2 straight j with hat on top space plus space straight k with hat on top right parenthesis space plus 3 left parenthesis negative 3 bold i with hat on top space minus 2 stack bold j bold space with hat on top plus bold k with hat on top right parenthesis over denominator 1 plus 3 end fraction equals space 1 fourth space left parenthesis negative 8 bold i with bold hat on top minus 4 bold j with bold hat on top space plus 4 bold k with bold hat on top right parenthesis equals negative 2 bold i with hat on top space minus bold j with bold hat on top space plus bold k with hat on top$
Point to know:
The centre of mass changes its position only under the translatory motion. There is no effect of rotatory motion on centre of mass of the body.

Some More Questions From Motion in A Plane Chapter

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

Two bodies of mass 1 kg have position vectors, respectively.The centre of mass of this system has a position vector

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.