Centre of Mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365736 \((n-1)\) equal point masses each of mass \(m\) are placed at the vertices of a regular \({\rm{n}}\)-polygon. The vacant vertex has a position vector \(a\) with respect to the centre of the polygon. Find the positive vector of centre of mass.

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

365737 Four particles, each of mass \(1\;kg\) are placed at the corners of a square \(O A B C\) of side \(1\;m\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

1 \(\hat{i}+\hat{j}\)
2 \(\dfrac{1}{2}(\hat{i}+\hat{j})\)
3 \((\hat{i}-\hat{j})\)
4 \(\dfrac{1}{2}(\hat{i}-\hat{j})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365738 Two objects of masses \(10\;kg\) and \(20\;kg\) respectively are connected to the two ends of a rigid rod of length \(10\;m\) with negligible mass. The distance of the center of mass of the system from the \(10\;kg\) mass is

1 \(\frac{{20}}{3}\;m\)
2 \(10\;m\)
3 \(5\;m\)
4 \(\frac{{10}}{3}\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365739 A system consists of two masses connected by a massless rod lies along \(x\)-axis. The distance of centre of mass from \(O\) is
supporting img

1 \(2\;m\)
2 \(3\;m\)
3 \(5\;m\)
4 \(7\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365740 Three masses are placed on the \(x\)-axis, \(300 g\) at origin, \(500 \mathrm{~g}\) at \(x=40 \mathrm{~cm}\) and \(400 \mathrm{~g}\) at \(x = 70\;\,cm\). The distance of the centre of mass from the origin is

1 \(45\;\,cm\)
2 \(40\;\,cm\)
3 \(30\;\,cm\)
4 \(50\;\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365736 \((n-1)\) equal point masses each of mass \(m\) are placed at the vertices of a regular \({\rm{n}}\)-polygon. The vacant vertex has a position vector \(a\) with respect to the centre of the polygon. Find the positive vector of centre of mass.

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

365737 Four particles, each of mass \(1\;kg\) are placed at the corners of a square \(O A B C\) of side \(1\;m\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

1 \(\hat{i}+\hat{j}\)
2 \(\dfrac{1}{2}(\hat{i}+\hat{j})\)
3 \((\hat{i}-\hat{j})\)
4 \(\dfrac{1}{2}(\hat{i}-\hat{j})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365738 Two objects of masses \(10\;kg\) and \(20\;kg\) respectively are connected to the two ends of a rigid rod of length \(10\;m\) with negligible mass. The distance of the center of mass of the system from the \(10\;kg\) mass is

1 \(\frac{{20}}{3}\;m\)
2 \(10\;m\)
3 \(5\;m\)
4 \(\frac{{10}}{3}\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365739 A system consists of two masses connected by a massless rod lies along \(x\)-axis. The distance of centre of mass from \(O\) is
supporting img

1 \(2\;m\)
2 \(3\;m\)
3 \(5\;m\)
4 \(7\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365740 Three masses are placed on the \(x\)-axis, \(300 g\) at origin, \(500 \mathrm{~g}\) at \(x=40 \mathrm{~cm}\) and \(400 \mathrm{~g}\) at \(x = 70\;\,cm\). The distance of the centre of mass from the origin is

1 \(45\;\,cm\)
2 \(40\;\,cm\)
3 \(30\;\,cm\)
4 \(50\;\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365736 \((n-1)\) equal point masses each of mass \(m\) are placed at the vertices of a regular \({\rm{n}}\)-polygon. The vacant vertex has a position vector \(a\) with respect to the centre of the polygon. Find the positive vector of centre of mass.

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

365737 Four particles, each of mass \(1\;kg\) are placed at the corners of a square \(O A B C\) of side \(1\;m\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

1 \(\hat{i}+\hat{j}\)
2 \(\dfrac{1}{2}(\hat{i}+\hat{j})\)
3 \((\hat{i}-\hat{j})\)
4 \(\dfrac{1}{2}(\hat{i}-\hat{j})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365738 Two objects of masses \(10\;kg\) and \(20\;kg\) respectively are connected to the two ends of a rigid rod of length \(10\;m\) with negligible mass. The distance of the center of mass of the system from the \(10\;kg\) mass is

1 \(\frac{{20}}{3}\;m\)
2 \(10\;m\)
3 \(5\;m\)
4 \(\frac{{10}}{3}\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365739 A system consists of two masses connected by a massless rod lies along \(x\)-axis. The distance of centre of mass from \(O\) is
supporting img

1 \(2\;m\)
2 \(3\;m\)
3 \(5\;m\)
4 \(7\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365740 Three masses are placed on the \(x\)-axis, \(300 g\) at origin, \(500 \mathrm{~g}\) at \(x=40 \mathrm{~cm}\) and \(400 \mathrm{~g}\) at \(x = 70\;\,cm\). The distance of the centre of mass from the origin is

1 \(45\;\,cm\)
2 \(40\;\,cm\)
3 \(30\;\,cm\)
4 \(50\;\,cm\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365736 \((n-1)\) equal point masses each of mass \(m\) are placed at the vertices of a regular \({\rm{n}}\)-polygon. The vacant vertex has a position vector \(a\) with respect to the centre of the polygon. Find the positive vector of centre of mass.

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

365737 Four particles, each of mass \(1\;kg\) are placed at the corners of a square \(O A B C\) of side \(1\;m\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

1 \(\hat{i}+\hat{j}\)
2 \(\dfrac{1}{2}(\hat{i}+\hat{j})\)
3 \((\hat{i}-\hat{j})\)
4 \(\dfrac{1}{2}(\hat{i}-\hat{j})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365738 Two objects of masses \(10\;kg\) and \(20\;kg\) respectively are connected to the two ends of a rigid rod of length \(10\;m\) with negligible mass. The distance of the center of mass of the system from the \(10\;kg\) mass is

1 \(\frac{{20}}{3}\;m\)
2 \(10\;m\)
3 \(5\;m\)
4 \(\frac{{10}}{3}\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365739 A system consists of two masses connected by a massless rod lies along \(x\)-axis. The distance of centre of mass from \(O\) is
supporting img

1 \(2\;m\)
2 \(3\;m\)
3 \(5\;m\)
4 \(7\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365740 Three masses are placed on the \(x\)-axis, \(300 g\) at origin, \(500 \mathrm{~g}\) at \(x=40 \mathrm{~cm}\) and \(400 \mathrm{~g}\) at \(x = 70\;\,cm\). The distance of the centre of mass from the origin is

1 \(45\;\,cm\)
2 \(40\;\,cm\)
3 \(30\;\,cm\)
4 \(50\;\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365736 \((n-1)\) equal point masses each of mass \(m\) are placed at the vertices of a regular \({\rm{n}}\)-polygon. The vacant vertex has a position vector \(a\) with respect to the centre of the polygon. Find the positive vector of centre of mass.

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

365737 Four particles, each of mass \(1\;kg\) are placed at the corners of a square \(O A B C\) of side \(1\;m\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

1 \(\hat{i}+\hat{j}\)
2 \(\dfrac{1}{2}(\hat{i}+\hat{j})\)
3 \((\hat{i}-\hat{j})\)
4 \(\dfrac{1}{2}(\hat{i}-\hat{j})\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365738 Two objects of masses \(10\;kg\) and \(20\;kg\) respectively are connected to the two ends of a rigid rod of length \(10\;m\) with negligible mass. The distance of the center of mass of the system from the \(10\;kg\) mass is

1 \(\frac{{20}}{3}\;m\)
2 \(10\;m\)
3 \(5\;m\)
4 \(\frac{{10}}{3}\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365739 A system consists of two masses connected by a massless rod lies along \(x\)-axis. The distance of centre of mass from \(O\) is
supporting img

1 \(2\;m\)
2 \(3\;m\)
3 \(5\;m\)
4 \(7\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365740 Three masses are placed on the \(x\)-axis, \(300 g\) at origin, \(500 \mathrm{~g}\) at \(x=40 \mathrm{~cm}\) and \(400 \mathrm{~g}\) at \(x = 70\;\,cm\). The distance of the centre of mass from the origin is

1 \(45\;\,cm\)
2 \(40\;\,cm\)
3 \(30\;\,cm\)
4 \(50\;\,cm\)