The co-ordinates of the center of mass ${\overrightarrow r _{cm}} = \frac{{0 + 150 \times \left( {\frac{1}{2}i + \frac{{\sqrt 3 }}{2}\hat j}

$\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{4}\,m} \right)$

The co-ordinates of the center of mass ${\overrightarrow r _{cm}} = \frac{{0 + 150 \times \left( {\frac{1}{2}i + \frac{{\sqrt 3 }}{2}\hat j} \right) + 100 \times \hat i}}{{300}}$ ${\overrightarrow r _{cm}} = \frac{7}{{12}}\hat i + \frac{{\sqrt 3 }}{4}\hat j$ $\therefore \,\,Co - ordinate\left( {\frac{7}{{12}},\frac{{\sqrt 3 }}{4}} \right)m$

6.System of Particles and Rotational MotionDifficult

Three particles of masses $50\, g$, $100\, g$ and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be

[JEE MAIN 2019]

A
$\left( {\frac{{\sqrt 3 }}{7}\,m,\,\frac{7}{{12}}\,m} \right)$
B
$\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{8}\,m} \right)$
C
$\left( {\frac{{\sqrt 3 }}{4}\,m,\,\frac{5}{{12}}\,m} \right)$
D
$\left( {\frac{7}{{12}}m,\,\frac{{\sqrt 3 }}{4}\,m} \right)$

Std 11
Physics

A $T$ shaped object with dimensions shown in the figure, is lying a smooth floor. A force $'\vec F'$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$

Difficult

[AIEEE 2005]

View Solution

When does a body (system) have different centre of gravity and centre of mass ?

Medium

View Solution

A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by

Difficult

View Solution

Four particles $A, B, C$ and $D$ with masses $m_A=m, m_B=2m, m_C=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

Difficult

[JEE MAIN 2019]

View Solution

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1\ \mathring A $. Given, mass of carbon atom is $12\ a.m.u.$ and mass of oxygen atom is $16\ a.m.u.$, calculate the position of the center of mass of the carbon monoxide molecule

Medium

View Solution

Three particles of masses $50\, g$, $100\, g$ and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be

Similar Questions

A $T$ shaped object with dimensions shown in the figure, is lying a smooth floor. A force $'\vec F'$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$

When does a body (system) have different centre of gravity and centre of mass ?

A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by

Four particles $A, B, C$ and $D$ with masses $m_A=m, m_B=2m, m_C=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1\ \mathring A $. Given, mass of carbon atom is $12\ a.m.u.$ and mass of oxygen atom is $16\ a.m.u.$, calculate the position of the center of mass of the carbon monoxide molecule