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Center of Mass as an Average Point

The position ...

Question

The position vector of center of mass of 'n' particles is a weighted average of the position vectors of the particles making up the system.

A

True

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B

False

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Solution

The correct option is A True

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Similar questions

Q. Two particles of mass

1 k g

3 k g

have position vectors

2 ¯ i + 3 ¯ j + 4 ¯ ¯ ¯ k

- 2 ¯ i + 3 ¯ j - 4 ¯ ¯ ¯ k

respectively. The position vector of centre of mass of the system is:

Q. Three particles, each of mass m are placed at the vertices of a right angled triangle as shown in figure. The position vector of the center of mass of the system is:
(O is the origin and

^i,^j,^k

are unit vectors)

Q. The position vectors of two identical particles with respect to the origin in three-dimensional coordinate system are

r_{1}

r_{2}

. The position vector of centre of mass of the system is given by:

Q. The position vector of three particles of mass

m_{1} = 3 kg, m_{2} = 4 kg

m_{3} = 1 kg

_{1} = (2^i +^j + 3^k) m,_{2} = (^i - 3^j + 2^k) m

_{3} = (3^i - 2^j -^k) m

respectively. Find the position vector of centre of mass of the system of particles.

Q. A system of particles in motion has mass center G as shown in the figure. The particle i has mass

m_{i}

and its position with respect to a fixed point O is given by the position vector

ρ_{i}

. The position of the particle with respect to g is given by the vector

ρ_{i}

. The time rate of change of the angular momentum of the system of particles about G is (The quantity

_{i}

indicates second derivative of

ρ_{i}

with respect to time and likewise for

r_{i}

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