00. Centre of Mass
Rotational Motion

149725 Three identical spheres each of mass \(1 \mathrm{~kg}\) are placed touching one another with their centres in a straight line. Their centres are marked as \(A, B, C\), respectively. The distance of centre of mass of the system from \(A\) is

1 \(\frac{\mathrm{AB}+\mathrm{AC}}{2}\)
2 \(\frac{\mathrm{AB}+\mathrm{BC}}{2}\)
3 \(\frac{\mathrm{AC}-\mathrm{AB}}{3}\)
4 \(\frac{\mathrm{AB}+\mathrm{AC}}{3}\)
Rotational Motion

149726 A cheetah, weighing \(150 \mathrm{~kg}\), chases a deer, weighing \(30 \mathrm{~kg}\), in a straight path. The speed of the cheetah is \(20 \mathrm{~m} / \mathrm{s}\) and that of the deer is 25 \(\mathrm{m} / \mathrm{s}\). The approximate speed of the centre of mass of the pair is

1 \(21 \mathrm{~m} / \mathrm{s}\)
2 \(24 \mathrm{~m} / \mathrm{s}\)
3 \(26 \mathrm{~m} / \mathrm{s}\)
4 zero
Rotational Motion

149727 Two bodies of masses \(m_{1}\) and \(m_{2}\) are separated by a distance \(R\). The distance of the centre of mass of the bodies from the mass \(m_{1}\) is

1 \(\frac{m_{2} R}{m_{1}+m_{2}}\)
2 \(\frac{\mathrm{m}_{1} \mathrm{R}}{\mathrm{m}_{1}+\mathrm{m}_{2}}\)
3 \(\frac{m_{1} m_{2}}{m_{1}+m_{2}} R\)
4 \(\frac{m_{1}+m_{2}}{m_{1}} R\)
Rotational Motion

149728 A large number of particles are placed around the origin, each at a distance \(R\) from the origin. The distance of the centre of mass of the system from the origin is

1 equal to \(R\)
2 less than equal to \(\mathrm{R}\)
3 greater than \(\mathrm{R}\)
4 greater than equal to \(\mathrm{R}\)
Rotational Motion

149725 Three identical spheres each of mass \(1 \mathrm{~kg}\) are placed touching one another with their centres in a straight line. Their centres are marked as \(A, B, C\), respectively. The distance of centre of mass of the system from \(A\) is

1 \(\frac{\mathrm{AB}+\mathrm{AC}}{2}\)
2 \(\frac{\mathrm{AB}+\mathrm{BC}}{2}\)
3 \(\frac{\mathrm{AC}-\mathrm{AB}}{3}\)
4 \(\frac{\mathrm{AB}+\mathrm{AC}}{3}\)
Rotational Motion

149726 A cheetah, weighing \(150 \mathrm{~kg}\), chases a deer, weighing \(30 \mathrm{~kg}\), in a straight path. The speed of the cheetah is \(20 \mathrm{~m} / \mathrm{s}\) and that of the deer is 25 \(\mathrm{m} / \mathrm{s}\). The approximate speed of the centre of mass of the pair is

1 \(21 \mathrm{~m} / \mathrm{s}\)
2 \(24 \mathrm{~m} / \mathrm{s}\)
3 \(26 \mathrm{~m} / \mathrm{s}\)
4 zero
Rotational Motion

149727 Two bodies of masses \(m_{1}\) and \(m_{2}\) are separated by a distance \(R\). The distance of the centre of mass of the bodies from the mass \(m_{1}\) is

1 \(\frac{m_{2} R}{m_{1}+m_{2}}\)
2 \(\frac{\mathrm{m}_{1} \mathrm{R}}{\mathrm{m}_{1}+\mathrm{m}_{2}}\)
3 \(\frac{m_{1} m_{2}}{m_{1}+m_{2}} R\)
4 \(\frac{m_{1}+m_{2}}{m_{1}} R\)
Rotational Motion

149728 A large number of particles are placed around the origin, each at a distance \(R\) from the origin. The distance of the centre of mass of the system from the origin is

1 equal to \(R\)
2 less than equal to \(\mathrm{R}\)
3 greater than \(\mathrm{R}\)
4 greater than equal to \(\mathrm{R}\)
Rotational Motion

149725 Three identical spheres each of mass \(1 \mathrm{~kg}\) are placed touching one another with their centres in a straight line. Their centres are marked as \(A, B, C\), respectively. The distance of centre of mass of the system from \(A\) is

1 \(\frac{\mathrm{AB}+\mathrm{AC}}{2}\)
2 \(\frac{\mathrm{AB}+\mathrm{BC}}{2}\)
3 \(\frac{\mathrm{AC}-\mathrm{AB}}{3}\)
4 \(\frac{\mathrm{AB}+\mathrm{AC}}{3}\)
Rotational Motion

149726 A cheetah, weighing \(150 \mathrm{~kg}\), chases a deer, weighing \(30 \mathrm{~kg}\), in a straight path. The speed of the cheetah is \(20 \mathrm{~m} / \mathrm{s}\) and that of the deer is 25 \(\mathrm{m} / \mathrm{s}\). The approximate speed of the centre of mass of the pair is

1 \(21 \mathrm{~m} / \mathrm{s}\)
2 \(24 \mathrm{~m} / \mathrm{s}\)
3 \(26 \mathrm{~m} / \mathrm{s}\)
4 zero
Rotational Motion

149727 Two bodies of masses \(m_{1}\) and \(m_{2}\) are separated by a distance \(R\). The distance of the centre of mass of the bodies from the mass \(m_{1}\) is

1 \(\frac{m_{2} R}{m_{1}+m_{2}}\)
2 \(\frac{\mathrm{m}_{1} \mathrm{R}}{\mathrm{m}_{1}+\mathrm{m}_{2}}\)
3 \(\frac{m_{1} m_{2}}{m_{1}+m_{2}} R\)
4 \(\frac{m_{1}+m_{2}}{m_{1}} R\)
Rotational Motion

149728 A large number of particles are placed around the origin, each at a distance \(R\) from the origin. The distance of the centre of mass of the system from the origin is

1 equal to \(R\)
2 less than equal to \(\mathrm{R}\)
3 greater than \(\mathrm{R}\)
4 greater than equal to \(\mathrm{R}\)
Rotational Motion

149725 Three identical spheres each of mass \(1 \mathrm{~kg}\) are placed touching one another with their centres in a straight line. Their centres are marked as \(A, B, C\), respectively. The distance of centre of mass of the system from \(A\) is

1 \(\frac{\mathrm{AB}+\mathrm{AC}}{2}\)
2 \(\frac{\mathrm{AB}+\mathrm{BC}}{2}\)
3 \(\frac{\mathrm{AC}-\mathrm{AB}}{3}\)
4 \(\frac{\mathrm{AB}+\mathrm{AC}}{3}\)
Rotational Motion

149726 A cheetah, weighing \(150 \mathrm{~kg}\), chases a deer, weighing \(30 \mathrm{~kg}\), in a straight path. The speed of the cheetah is \(20 \mathrm{~m} / \mathrm{s}\) and that of the deer is 25 \(\mathrm{m} / \mathrm{s}\). The approximate speed of the centre of mass of the pair is

1 \(21 \mathrm{~m} / \mathrm{s}\)
2 \(24 \mathrm{~m} / \mathrm{s}\)
3 \(26 \mathrm{~m} / \mathrm{s}\)
4 zero
Rotational Motion

149727 Two bodies of masses \(m_{1}\) and \(m_{2}\) are separated by a distance \(R\). The distance of the centre of mass of the bodies from the mass \(m_{1}\) is

1 \(\frac{m_{2} R}{m_{1}+m_{2}}\)
2 \(\frac{\mathrm{m}_{1} \mathrm{R}}{\mathrm{m}_{1}+\mathrm{m}_{2}}\)
3 \(\frac{m_{1} m_{2}}{m_{1}+m_{2}} R\)
4 \(\frac{m_{1}+m_{2}}{m_{1}} R\)
Rotational Motion

149728 A large number of particles are placed around the origin, each at a distance \(R\) from the origin. The distance of the centre of mass of the system from the origin is

1 equal to \(R\)
2 less than equal to \(\mathrm{R}\)
3 greater than \(\mathrm{R}\)
4 greater than equal to \(\mathrm{R}\)