Zigya Logo

Chapter Chosen

Motion in A Plane

Book Chosen

Physics Part I

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

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

B.

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.

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.

888 Views

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


814 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views