Centre of Mass
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365724 Particles of masses \(m, 2 m, 3 m, \ldots . n m\) grams are placed on the same line at distance \(l,\,2l,\,3l, \ldots \ldots .nl\,cm\) from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is

1 \(\dfrac{1}{n+1}\)
2 \(\dfrac{(2 n+1) l}{3}\)
3 \(\dfrac{2 l}{n\left(n^{2}+1\right)}\)
4 \(\dfrac{n\left(n^{2}+1\right) l}{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365725 In the \(HCL\) molecule, the separation between the nuclei of the two atoms is about \(1.27\mathop {{\rm{ }}A}\limits^o {\mkern 1mu} \,\,{\mkern 1mu} 1\mathop A\limits^o = {10^{ - 10}}\;m\). Find the approximate location of the centre of mass of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucles.

1 \({r_{CM}} = 2.22\mathop A\limits^o \)
2 \({r_{CM}} = 1.24\mathop A\limits^o \)
3 \({r_{CM}} = 3.24\mathop A\limits^o \)
4 \({r_{CM}} = 0.24\mathop A\limits^o \)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365726 A rigid body consists of a \(3\;kg\) mass located at \(\vec{r}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2\;kg\) mass located at \(\vec{r}=(4 \hat{i}+2 \hat{j}) m\). The position of centre of mass is

1 \(\left(\dfrac{14}{5} \hat{j}+\dfrac{19}{5} \hat{i}\right) m\)
2 \(\left(\dfrac{14}{5} \hat{i}+\dfrac{19}{5} \hat{j}\right) m\)
3 \(\left(\dfrac{19}{5} \hat{i}+\dfrac{14}{5} \hat{j}\right) m\)
4 \(0\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365727 A system consists of three particles, each of mass \(m\) and located at \((1,1),(2,2)\) and \((3,3)\). The coordinates of the centre of mass are

1 \((1,1)\)
2 \((2,2)\)
3 \((3,3)\)
4 \((6,6)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365724 Particles of masses \(m, 2 m, 3 m, \ldots . n m\) grams are placed on the same line at distance \(l,\,2l,\,3l, \ldots \ldots .nl\,cm\) from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is

1 \(\dfrac{1}{n+1}\)
2 \(\dfrac{(2 n+1) l}{3}\)
3 \(\dfrac{2 l}{n\left(n^{2}+1\right)}\)
4 \(\dfrac{n\left(n^{2}+1\right) l}{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365725 In the \(HCL\) molecule, the separation between the nuclei of the two atoms is about \(1.27\mathop {{\rm{ }}A}\limits^o {\mkern 1mu} \,\,{\mkern 1mu} 1\mathop A\limits^o = {10^{ - 10}}\;m\). Find the approximate location of the centre of mass of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucles.

1 \({r_{CM}} = 2.22\mathop A\limits^o \)
2 \({r_{CM}} = 1.24\mathop A\limits^o \)
3 \({r_{CM}} = 3.24\mathop A\limits^o \)
4 \({r_{CM}} = 0.24\mathop A\limits^o \)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365726 A rigid body consists of a \(3\;kg\) mass located at \(\vec{r}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2\;kg\) mass located at \(\vec{r}=(4 \hat{i}+2 \hat{j}) m\). The position of centre of mass is

1 \(\left(\dfrac{14}{5} \hat{j}+\dfrac{19}{5} \hat{i}\right) m\)
2 \(\left(\dfrac{14}{5} \hat{i}+\dfrac{19}{5} \hat{j}\right) m\)
3 \(\left(\dfrac{19}{5} \hat{i}+\dfrac{14}{5} \hat{j}\right) m\)
4 \(0\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365727 A system consists of three particles, each of mass \(m\) and located at \((1,1),(2,2)\) and \((3,3)\). The coordinates of the centre of mass are

1 \((1,1)\)
2 \((2,2)\)
3 \((3,3)\)
4 \((6,6)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365724 Particles of masses \(m, 2 m, 3 m, \ldots . n m\) grams are placed on the same line at distance \(l,\,2l,\,3l, \ldots \ldots .nl\,cm\) from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is

1 \(\dfrac{1}{n+1}\)
2 \(\dfrac{(2 n+1) l}{3}\)
3 \(\dfrac{2 l}{n\left(n^{2}+1\right)}\)
4 \(\dfrac{n\left(n^{2}+1\right) l}{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365725 In the \(HCL\) molecule, the separation between the nuclei of the two atoms is about \(1.27\mathop {{\rm{ }}A}\limits^o {\mkern 1mu} \,\,{\mkern 1mu} 1\mathop A\limits^o = {10^{ - 10}}\;m\). Find the approximate location of the centre of mass of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucles.

1 \({r_{CM}} = 2.22\mathop A\limits^o \)
2 \({r_{CM}} = 1.24\mathop A\limits^o \)
3 \({r_{CM}} = 3.24\mathop A\limits^o \)
4 \({r_{CM}} = 0.24\mathop A\limits^o \)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365726 A rigid body consists of a \(3\;kg\) mass located at \(\vec{r}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2\;kg\) mass located at \(\vec{r}=(4 \hat{i}+2 \hat{j}) m\). The position of centre of mass is

1 \(\left(\dfrac{14}{5} \hat{j}+\dfrac{19}{5} \hat{i}\right) m\)
2 \(\left(\dfrac{14}{5} \hat{i}+\dfrac{19}{5} \hat{j}\right) m\)
3 \(\left(\dfrac{19}{5} \hat{i}+\dfrac{14}{5} \hat{j}\right) m\)
4 \(0\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365727 A system consists of three particles, each of mass \(m\) and located at \((1,1),(2,2)\) and \((3,3)\). The coordinates of the centre of mass are

1 \((1,1)\)
2 \((2,2)\)
3 \((3,3)\)
4 \((6,6)\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365724 Particles of masses \(m, 2 m, 3 m, \ldots . n m\) grams are placed on the same line at distance \(l,\,2l,\,3l, \ldots \ldots .nl\,cm\) from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is

1 \(\dfrac{1}{n+1}\)
2 \(\dfrac{(2 n+1) l}{3}\)
3 \(\dfrac{2 l}{n\left(n^{2}+1\right)}\)
4 \(\dfrac{n\left(n^{2}+1\right) l}{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365725 In the \(HCL\) molecule, the separation between the nuclei of the two atoms is about \(1.27\mathop {{\rm{ }}A}\limits^o {\mkern 1mu} \,\,{\mkern 1mu} 1\mathop A\limits^o = {10^{ - 10}}\;m\). Find the approximate location of the centre of mass of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucles.

1 \({r_{CM}} = 2.22\mathop A\limits^o \)
2 \({r_{CM}} = 1.24\mathop A\limits^o \)
3 \({r_{CM}} = 3.24\mathop A\limits^o \)
4 \({r_{CM}} = 0.24\mathop A\limits^o \)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365726 A rigid body consists of a \(3\;kg\) mass located at \(\vec{r}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2\;kg\) mass located at \(\vec{r}=(4 \hat{i}+2 \hat{j}) m\). The position of centre of mass is

1 \(\left(\dfrac{14}{5} \hat{j}+\dfrac{19}{5} \hat{i}\right) m\)
2 \(\left(\dfrac{14}{5} \hat{i}+\dfrac{19}{5} \hat{j}\right) m\)
3 \(\left(\dfrac{19}{5} \hat{i}+\dfrac{14}{5} \hat{j}\right) m\)
4 \(0\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365727 A system consists of three particles, each of mass \(m\) and located at \((1,1),(2,2)\) and \((3,3)\). The coordinates of the centre of mass are

1 \((1,1)\)
2 \((2,2)\)
3 \((3,3)\)
4 \((6,6)\)