Question

1)two particles of equal mass are at distance of X1 and X2 from the origin of a co-ordinate system find the distance of the centre mass from the origin.
2)write expression for the position vector of the centre of mass of a system consisting of three object in terms of the masses and position vectors.

please answer these questions. Class 11 physics system of particles and rotational motion.​

Answer 1

Answer:

this is your answer hope it helps you

Answer 2

Answer:

1) The center of mass from the origin of two equal masses is given by $x_{cm} = \frac{x_{1} +x_{2} }{2}$

2) The expression for the position vector of the center of mass of a system consisting of three objects in terms of the masses and position vectors is given by $x_{cm} =\frac{x_{1} m_{1} +x_{2} m_{2}+x_{3} m_{3} }{m_{1}+ m_{2} +m_{3} }$

Explanation:

The Centre of mass is the point where the whole mass of the body is supposed to be concentrated. For symmetrical bodies, it is present at the geometrical center of the body.

Now, the formula for the center of mass is given by,

$x_{cm} =\frac{x_{1} m_{1} +x_{2} m_{2} }{m_{1}+ m_{2} }$

where

Now, since the two masses are the same, then the formula becomes,

$x_{cm} =\frac{x_{1} m+x_{2} m }{m+ m}$

Then,

$x_{cm} = \frac{x_{1} +x_{2} }{2}$

Now, the expression for the position vector of the center of mass of a system consisting of three objects in terms of the masses and position vectors is given by :

$x_{cm} =\frac{x_{1} m_{1} +x_{2} m_{2}+x_{3} m_{3} }{m_{1}+ m_{2} +m_{3} }$

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