Find the centre of mass of a triangular lamina.
Find the centre of mass of a triangular lamina.
Answer The lamina ($\Delta LMN$) may be subdivided into narrow strips each parallel to the base $(MN)$ as shown in Figure
By symmetry each strip has its centre of mass at its midpoint. If we join the midpoint of all the strips we get the median $LP$. The centre of mass of the triangle as a whole therefore, has to lie on the median $LP$. Similarly, we can argue that it lies on the median $MQ$ and $NR$ This means the centre of mass lies on the point of concurrence of the medians, i.e. on the centroid $G$ of the triangle.
Similar Questions
Consider following statements
$[1]$ $CM$ of a uniform semicircular disc of radius $R = 2R/\pi$ from the centre
$[2]$ $CM$ of a uniform semicircular ring of radius $R = 4R/3 \pi$ from the centre
$[3]$ $CM$ of a solid hemisphere of radius $R = 4R/3 \pi$ from the centre
$[4]$ $CM$ of a hemisphere shell of radius $R = R/2$ from the centre Which statements are correct?
Consider following statements
$[1]$ $CM$ of a uniform semicircular disc of radius $R = 2R/\pi$ from the centre
$[2]$ $CM$ of a uniform semicircular ring of radius $R = 4R/3 \pi$ from the centre
$[3]$ $CM$ of a solid hemisphere of radius $R = 4R/3 \pi$ from the centre
$[4]$ $CM$ of a hemisphere shell of radius $R = R/2$ from the centre Which statements are correct?
Explain the theoretical method for estimation of the centre of mass of a solid body.
Explain the theoretical method for estimation of the centre of mass of a solid body.
Obtain an expression for the position vector of centre of mass of a system n particles in two dimension.
Obtain an expression for the position vector of centre of mass of a system n particles in two dimension.
Two particle of masses $1\,kg$ and $3\,kg$ have position vector $2\hat i + 3\hat j + 4\hat k$ and $ - 2\hat i + 3\hat j - 4\hat k$ respectively. The centre of mass has a position vector
Two particle of masses $1\,kg$ and $3\,kg$ have position vector $2\hat i + 3\hat j + 4\hat k$ and $ - 2\hat i + 3\hat j - 4\hat k$ respectively. The centre of mass has a position vector
Five masses are placed in a plane as shown in figure. The coordinates of the centre of mass are nearest to.
Five masses are placed in a plane as shown in figure. The coordinates of the centre of mass are nearest to.
- [AIIMS 2017]