00. Centre of Mass
Rotational Motion

269484 If three particles of masses\(2 \mathrm{~kg}, 1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are placed at corners of an equilateral triangle of perimeter \(6 \mathrm{~m}\) then the distance of centre of mass which is at origin of particles from \(1 \mathrm{~kg}\) mass is (approximately) ( Assume \(2 \mathrm{~kg}\) on \(\mathrm{x}\)-axis

1 \(\sqrt{6} \mathrm{~m}\)
2 \(\sqrt{2} m\)
3 \(\frac{1}{\sqrt{2}} m\)
4 \(2 m\)
Rotational Motion

269485 Six identical particles each of mass '\(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is

1 \(\mathrm{L}\)
2 \(6 \mathrm{~L} / 7\)
3 \(\mathrm{L} / 7\)
4 \(\frac{L}{\sqrt{3}}\)
Rotational Motion

269486 A bomb of mass '\(m\) ' at rest at the coordinate origin explodes into three equal pieces. At a certain instant one piece is on the \(x\)-axis at \(x=40 \mathrm{~cm}\) and another is at \(x=20 \mathrm{~cm}\), \(y=-60 \mathrm{~cm}\). The position of the third piece is

1 \(x=60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
2 \(x=-60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
3 \(x=-60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
4 \(x=60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
Rotational Motion

269487 Particles of masses\(m, 2 m, 3 m\). nm gram are placed on the same line at distances, \(l\), \(21,3 I\), \(\mathrm{nl} \mathrm{cm}\) from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) in

1 \(\frac{(2 n+1) l}{3}\)
2 \(\frac{l}{n+1}\)
3 \(\frac{n\left(n^{2}+l\right) l}{2}\)
4 \(\frac{2 l}{n\left(n^{2}+l\right) l}\)
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Rotational Motion

269484 If three particles of masses\(2 \mathrm{~kg}, 1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are placed at corners of an equilateral triangle of perimeter \(6 \mathrm{~m}\) then the distance of centre of mass which is at origin of particles from \(1 \mathrm{~kg}\) mass is (approximately) ( Assume \(2 \mathrm{~kg}\) on \(\mathrm{x}\)-axis

1 \(\sqrt{6} \mathrm{~m}\)
2 \(\sqrt{2} m\)
3 \(\frac{1}{\sqrt{2}} m\)
4 \(2 m\)
Rotational Motion

269485 Six identical particles each of mass '\(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is

1 \(\mathrm{L}\)
2 \(6 \mathrm{~L} / 7\)
3 \(\mathrm{L} / 7\)
4 \(\frac{L}{\sqrt{3}}\)
Rotational Motion

269486 A bomb of mass '\(m\) ' at rest at the coordinate origin explodes into three equal pieces. At a certain instant one piece is on the \(x\)-axis at \(x=40 \mathrm{~cm}\) and another is at \(x=20 \mathrm{~cm}\), \(y=-60 \mathrm{~cm}\). The position of the third piece is

1 \(x=60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
2 \(x=-60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
3 \(x=-60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
4 \(x=60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
Rotational Motion

269487 Particles of masses\(m, 2 m, 3 m\). nm gram are placed on the same line at distances, \(l\), \(21,3 I\), \(\mathrm{nl} \mathrm{cm}\) from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) in

1 \(\frac{(2 n+1) l}{3}\)
2 \(\frac{l}{n+1}\)
3 \(\frac{n\left(n^{2}+l\right) l}{2}\)
4 \(\frac{2 l}{n\left(n^{2}+l\right) l}\)
Rotational Motion

269484 If three particles of masses\(2 \mathrm{~kg}, 1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are placed at corners of an equilateral triangle of perimeter \(6 \mathrm{~m}\) then the distance of centre of mass which is at origin of particles from \(1 \mathrm{~kg}\) mass is (approximately) ( Assume \(2 \mathrm{~kg}\) on \(\mathrm{x}\)-axis

1 \(\sqrt{6} \mathrm{~m}\)
2 \(\sqrt{2} m\)
3 \(\frac{1}{\sqrt{2}} m\)
4 \(2 m\)
Rotational Motion

269485 Six identical particles each of mass '\(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is

1 \(\mathrm{L}\)
2 \(6 \mathrm{~L} / 7\)
3 \(\mathrm{L} / 7\)
4 \(\frac{L}{\sqrt{3}}\)
Rotational Motion

269486 A bomb of mass '\(m\) ' at rest at the coordinate origin explodes into three equal pieces. At a certain instant one piece is on the \(x\)-axis at \(x=40 \mathrm{~cm}\) and another is at \(x=20 \mathrm{~cm}\), \(y=-60 \mathrm{~cm}\). The position of the third piece is

1 \(x=60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
2 \(x=-60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
3 \(x=-60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
4 \(x=60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
Rotational Motion

269487 Particles of masses\(m, 2 m, 3 m\). nm gram are placed on the same line at distances, \(l\), \(21,3 I\), \(\mathrm{nl} \mathrm{cm}\) from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) in

1 \(\frac{(2 n+1) l}{3}\)
2 \(\frac{l}{n+1}\)
3 \(\frac{n\left(n^{2}+l\right) l}{2}\)
4 \(\frac{2 l}{n\left(n^{2}+l\right) l}\)
Rotational Motion

269484 If three particles of masses\(2 \mathrm{~kg}, 1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are placed at corners of an equilateral triangle of perimeter \(6 \mathrm{~m}\) then the distance of centre of mass which is at origin of particles from \(1 \mathrm{~kg}\) mass is (approximately) ( Assume \(2 \mathrm{~kg}\) on \(\mathrm{x}\)-axis

1 \(\sqrt{6} \mathrm{~m}\)
2 \(\sqrt{2} m\)
3 \(\frac{1}{\sqrt{2}} m\)
4 \(2 m\)
Rotational Motion

269485 Six identical particles each of mass '\(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is

1 \(\mathrm{L}\)
2 \(6 \mathrm{~L} / 7\)
3 \(\mathrm{L} / 7\)
4 \(\frac{L}{\sqrt{3}}\)
Rotational Motion

269486 A bomb of mass '\(m\) ' at rest at the coordinate origin explodes into three equal pieces. At a certain instant one piece is on the \(x\)-axis at \(x=40 \mathrm{~cm}\) and another is at \(x=20 \mathrm{~cm}\), \(y=-60 \mathrm{~cm}\). The position of the third piece is

1 \(x=60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
2 \(x=-60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
3 \(x=-60 \mathrm{~cm}, y=60 \mathrm{~cm}\)
4 \(x=60 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
Rotational Motion

269487 Particles of masses\(m, 2 m, 3 m\). nm gram are placed on the same line at distances, \(l\), \(21,3 I\), \(\mathrm{nl} \mathrm{cm}\) from a fixed point. The distance of centre of mass of the particles from the fixed point in \(\mathrm{cm}\) in

1 \(\frac{(2 n+1) l}{3}\)
2 \(\frac{l}{n+1}\)
3 \(\frac{n\left(n^{2}+l\right) l}{2}\)
4 \(\frac{2 l}{n\left(n^{2}+l\right) l}\)