Figure shows a rectangular copper plate with is centre of mass at the origin $ O $ and side $ AB = 2BC = 2 m $ . If a quarter part of the plate (shown as shaded) is removed, the centre of mass of the remaining plate would lie at
Given, $AB = 2BC = 2m$ $\therefore BC=1\,m$ $\sigma$ be the mass per unit area $m_{1}=m_{2}=m_{3}=(1\times0.5) \sigma=0.5\sigma$ If $G\left(\bar{x}, \bar{y}\right)$ be the position of centre of mass, then $\bar{x}=\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3} x_{3}}{m_{1}+m_{2}+m_{3}}$ $=\frac{0.5\sigma\times0.5+0.5\sigma\times\left(-0.5\right)+0.5\sigma\times0.5}{0.5\sigma+0.5\sigma+0.5\sigma}$ $=\frac{0.5\sigma\times0.5}{3\times0.5\sigma}=\frac{1}{6}m$ $\bar{y}=\frac{m_{1}y_{1}+m_{2}y_{2}+m_{3}y_{3}}{m_{1}+m_{2}+m_{3}}$ $=\frac{0.5\sigma\times0.25+0.5\sigma\times0.25+0.5\sigma\times\left(-0.25\right)}{0.5\sigma+0.5\sigma+0.5\sigma}$ $=\frac{0.5\sigma\times0.25}{3\times0.5\sigma}=\frac{1}{12}m$
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.
