Centre of Mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365749 A circular plate of uniform thickness has a diameter of \(112\;cm.\) A circular portion of diameter \(84\;cm\) is removed from one edge as shown in the figure. The distance of centre of mass of the remaining portion from the centre of plate will be
supporting img

1 \(12\,cm\)
2 \(18\,cm\)
3 \(21\,cm\)
4 \(29\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365750 The \(x, y\) coordinates of the centre of mass of a uniform \(L\)-shaped lamina of mass \(3\;kg\) is
supporting img

1 \(\left(\dfrac{5}{6}, \dfrac{5}{6}\right)\)
2 \(\left(\dfrac{1}{2}, \dfrac{1}{2}\right)\)
3 \(\left(\dfrac{1}{5}, \dfrac{1}{5}\right)\)
4 \((1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365751 Three identical spheres, each of mass \(1\;kg\) are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked \(P,{\rm{ }}Q,{\rm{ }}R\) respectively, the distance of centre of mass of the system from \(P\) is
supporting img

1 \(\dfrac{P Q+P R+Q R}{3}\)
2 \(\dfrac{P Q+P R}{3}\)
3 \(\dfrac{P Q+Q R}{3}\)
4 \(\dfrac{P R+Q R}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365752 Two uniform rods of different materials \({M_{1}}\) and \({M_{2}}\) have lengths \({2 m}\) and \({4 m}\), respectively. The mass per unit length of rods \({M_{1}}\) and \({M_{2}}\) are \({1 {~kg} / {m}}\) and \({2 {~kg} / {m}}\), respectively. If the rods are arranged, as shown, the position of the centre of mass relative to \({O}\) point is
supporting img

1 \({4.9 m}\)
2 \({2 m}\)
3 \({3.4 m}\)
4 \({2.2 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365753 Three bricks each of length \(L\) and mass \(M\) are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
supporting img

1 \(\dfrac{L}{2}\)
2 \(\dfrac{L}{4}\)
3 \(\frac{3}{2}\;L\)
4 \(\frac{{11}}{{12}}\;L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365749 A circular plate of uniform thickness has a diameter of \(112\;cm.\) A circular portion of diameter \(84\;cm\) is removed from one edge as shown in the figure. The distance of centre of mass of the remaining portion from the centre of plate will be
supporting img

1 \(12\,cm\)
2 \(18\,cm\)
3 \(21\,cm\)
4 \(29\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365750 The \(x, y\) coordinates of the centre of mass of a uniform \(L\)-shaped lamina of mass \(3\;kg\) is
supporting img

1 \(\left(\dfrac{5}{6}, \dfrac{5}{6}\right)\)
2 \(\left(\dfrac{1}{2}, \dfrac{1}{2}\right)\)
3 \(\left(\dfrac{1}{5}, \dfrac{1}{5}\right)\)
4 \((1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365751 Three identical spheres, each of mass \(1\;kg\) are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked \(P,{\rm{ }}Q,{\rm{ }}R\) respectively, the distance of centre of mass of the system from \(P\) is
supporting img

1 \(\dfrac{P Q+P R+Q R}{3}\)
2 \(\dfrac{P Q+P R}{3}\)
3 \(\dfrac{P Q+Q R}{3}\)
4 \(\dfrac{P R+Q R}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365752 Two uniform rods of different materials \({M_{1}}\) and \({M_{2}}\) have lengths \({2 m}\) and \({4 m}\), respectively. The mass per unit length of rods \({M_{1}}\) and \({M_{2}}\) are \({1 {~kg} / {m}}\) and \({2 {~kg} / {m}}\), respectively. If the rods are arranged, as shown, the position of the centre of mass relative to \({O}\) point is
supporting img

1 \({4.9 m}\)
2 \({2 m}\)
3 \({3.4 m}\)
4 \({2.2 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365753 Three bricks each of length \(L\) and mass \(M\) are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
supporting img

1 \(\dfrac{L}{2}\)
2 \(\dfrac{L}{4}\)
3 \(\frac{3}{2}\;L\)
4 \(\frac{{11}}{{12}}\;L\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365749 A circular plate of uniform thickness has a diameter of \(112\;cm.\) A circular portion of diameter \(84\;cm\) is removed from one edge as shown in the figure. The distance of centre of mass of the remaining portion from the centre of plate will be
supporting img

1 \(12\,cm\)
2 \(18\,cm\)
3 \(21\,cm\)
4 \(29\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365750 The \(x, y\) coordinates of the centre of mass of a uniform \(L\)-shaped lamina of mass \(3\;kg\) is
supporting img

1 \(\left(\dfrac{5}{6}, \dfrac{5}{6}\right)\)
2 \(\left(\dfrac{1}{2}, \dfrac{1}{2}\right)\)
3 \(\left(\dfrac{1}{5}, \dfrac{1}{5}\right)\)
4 \((1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365751 Three identical spheres, each of mass \(1\;kg\) are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked \(P,{\rm{ }}Q,{\rm{ }}R\) respectively, the distance of centre of mass of the system from \(P\) is
supporting img

1 \(\dfrac{P Q+P R+Q R}{3}\)
2 \(\dfrac{P Q+P R}{3}\)
3 \(\dfrac{P Q+Q R}{3}\)
4 \(\dfrac{P R+Q R}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365752 Two uniform rods of different materials \({M_{1}}\) and \({M_{2}}\) have lengths \({2 m}\) and \({4 m}\), respectively. The mass per unit length of rods \({M_{1}}\) and \({M_{2}}\) are \({1 {~kg} / {m}}\) and \({2 {~kg} / {m}}\), respectively. If the rods are arranged, as shown, the position of the centre of mass relative to \({O}\) point is
supporting img

1 \({4.9 m}\)
2 \({2 m}\)
3 \({3.4 m}\)
4 \({2.2 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365753 Three bricks each of length \(L\) and mass \(M\) are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
supporting img

1 \(\dfrac{L}{2}\)
2 \(\dfrac{L}{4}\)
3 \(\frac{3}{2}\;L\)
4 \(\frac{{11}}{{12}}\;L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365749 A circular plate of uniform thickness has a diameter of \(112\;cm.\) A circular portion of diameter \(84\;cm\) is removed from one edge as shown in the figure. The distance of centre of mass of the remaining portion from the centre of plate will be
supporting img

1 \(12\,cm\)
2 \(18\,cm\)
3 \(21\,cm\)
4 \(29\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365750 The \(x, y\) coordinates of the centre of mass of a uniform \(L\)-shaped lamina of mass \(3\;kg\) is
supporting img

1 \(\left(\dfrac{5}{6}, \dfrac{5}{6}\right)\)
2 \(\left(\dfrac{1}{2}, \dfrac{1}{2}\right)\)
3 \(\left(\dfrac{1}{5}, \dfrac{1}{5}\right)\)
4 \((1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365751 Three identical spheres, each of mass \(1\;kg\) are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked \(P,{\rm{ }}Q,{\rm{ }}R\) respectively, the distance of centre of mass of the system from \(P\) is
supporting img

1 \(\dfrac{P Q+P R+Q R}{3}\)
2 \(\dfrac{P Q+P R}{3}\)
3 \(\dfrac{P Q+Q R}{3}\)
4 \(\dfrac{P R+Q R}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365752 Two uniform rods of different materials \({M_{1}}\) and \({M_{2}}\) have lengths \({2 m}\) and \({4 m}\), respectively. The mass per unit length of rods \({M_{1}}\) and \({M_{2}}\) are \({1 {~kg} / {m}}\) and \({2 {~kg} / {m}}\), respectively. If the rods are arranged, as shown, the position of the centre of mass relative to \({O}\) point is
supporting img

1 \({4.9 m}\)
2 \({2 m}\)
3 \({3.4 m}\)
4 \({2.2 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365753 Three bricks each of length \(L\) and mass \(M\) are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
supporting img

1 \(\dfrac{L}{2}\)
2 \(\dfrac{L}{4}\)
3 \(\frac{3}{2}\;L\)
4 \(\frac{{11}}{{12}}\;L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365749 A circular plate of uniform thickness has a diameter of \(112\;cm.\) A circular portion of diameter \(84\;cm\) is removed from one edge as shown in the figure. The distance of centre of mass of the remaining portion from the centre of plate will be
supporting img

1 \(12\,cm\)
2 \(18\,cm\)
3 \(21\,cm\)
4 \(29\,cm\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365750 The \(x, y\) coordinates of the centre of mass of a uniform \(L\)-shaped lamina of mass \(3\;kg\) is
supporting img

1 \(\left(\dfrac{5}{6}, \dfrac{5}{6}\right)\)
2 \(\left(\dfrac{1}{2}, \dfrac{1}{2}\right)\)
3 \(\left(\dfrac{1}{5}, \dfrac{1}{5}\right)\)
4 \((1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365751 Three identical spheres, each of mass \(1\;kg\) are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked \(P,{\rm{ }}Q,{\rm{ }}R\) respectively, the distance of centre of mass of the system from \(P\) is
supporting img

1 \(\dfrac{P Q+P R+Q R}{3}\)
2 \(\dfrac{P Q+P R}{3}\)
3 \(\dfrac{P Q+Q R}{3}\)
4 \(\dfrac{P R+Q R}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365752 Two uniform rods of different materials \({M_{1}}\) and \({M_{2}}\) have lengths \({2 m}\) and \({4 m}\), respectively. The mass per unit length of rods \({M_{1}}\) and \({M_{2}}\) are \({1 {~kg} / {m}}\) and \({2 {~kg} / {m}}\), respectively. If the rods are arranged, as shown, the position of the centre of mass relative to \({O}\) point is
supporting img

1 \({4.9 m}\)
2 \({2 m}\)
3 \({3.4 m}\)
4 \({2.2 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365753 Three bricks each of length \(L\) and mass \(M\) are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
supporting img

1 \(\dfrac{L}{2}\)
2 \(\dfrac{L}{4}\)
3 \(\frac{3}{2}\;L\)
4 \(\frac{{11}}{{12}}\;L\)