00. Centre of Mass
Rotational Motion

269546 Three identical particles each of mass \(0.1 \mathrm{~kg}\) are arranged at three corners of a square of side \(\sqrt{2} \mathrm{~m}\). The distance of the center of mass from the fourth corner is

1 \(2 / 3 \mathrm{~m}\)
2 \(4 / 3 \mathrm{~m}\)
3 \(1 \mathrm{~m}\)
4 \(8 / 3 \mathrm{~m}\)
Rotational Motion

269547 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 \(x=60 \mathrm{~cm}\) and another is at \(x=40 \mathrm{~cm}, y=60 \mathrm{~cm}\). The position of the third piece is

1 \(x=-100 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
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

269548 Masses \(1 \mathrm{~kg}, 1.5 \mathrm{~kg}, 2 \mathrm{~kg}\) and \(M \mathrm{~kg}\) are situated at \((2,1,1),(1,2,1),(2,-2,1)\) and \((-1,4,3)\).If their center of mass is situated at ( \(1,1,3 / 2\) ), the value of \(M\) is

1 \(1 \mathrm{~kg}\)
2 \(2 \mathrm{~kg}\)
3 \(1.5 \mathrm{~kg}\)
4 \(3 \mathrm{~kg}\)
Rotational Motion

269549 Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length ' \(L\) '. If the masses of any two adjacent particles are doubled. The shift in the centre of mass is

1 \(\frac{L}{8}\)
2 \(\frac{\sqrt{3} L}{8}\)
3 \(\frac{3 L}{16}\)
4 \(\frac{3 L}{4}\)
Rotational Motion

269546 Three identical particles each of mass \(0.1 \mathrm{~kg}\) are arranged at three corners of a square of side \(\sqrt{2} \mathrm{~m}\). The distance of the center of mass from the fourth corner is

1 \(2 / 3 \mathrm{~m}\)
2 \(4 / 3 \mathrm{~m}\)
3 \(1 \mathrm{~m}\)
4 \(8 / 3 \mathrm{~m}\)
Rotational Motion

269547 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 \(x=60 \mathrm{~cm}\) and another is at \(x=40 \mathrm{~cm}, y=60 \mathrm{~cm}\). The position of the third piece is

1 \(x=-100 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
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

269548 Masses \(1 \mathrm{~kg}, 1.5 \mathrm{~kg}, 2 \mathrm{~kg}\) and \(M \mathrm{~kg}\) are situated at \((2,1,1),(1,2,1),(2,-2,1)\) and \((-1,4,3)\).If their center of mass is situated at ( \(1,1,3 / 2\) ), the value of \(M\) is

1 \(1 \mathrm{~kg}\)
2 \(2 \mathrm{~kg}\)
3 \(1.5 \mathrm{~kg}\)
4 \(3 \mathrm{~kg}\)
Rotational Motion

269549 Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length ' \(L\) '. If the masses of any two adjacent particles are doubled. The shift in the centre of mass is

1 \(\frac{L}{8}\)
2 \(\frac{\sqrt{3} L}{8}\)
3 \(\frac{3 L}{16}\)
4 \(\frac{3 L}{4}\)
Rotational Motion

269546 Three identical particles each of mass \(0.1 \mathrm{~kg}\) are arranged at three corners of a square of side \(\sqrt{2} \mathrm{~m}\). The distance of the center of mass from the fourth corner is

1 \(2 / 3 \mathrm{~m}\)
2 \(4 / 3 \mathrm{~m}\)
3 \(1 \mathrm{~m}\)
4 \(8 / 3 \mathrm{~m}\)
Rotational Motion

269547 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 \(x=60 \mathrm{~cm}\) and another is at \(x=40 \mathrm{~cm}, y=60 \mathrm{~cm}\). The position of the third piece is

1 \(x=-100 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
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

269548 Masses \(1 \mathrm{~kg}, 1.5 \mathrm{~kg}, 2 \mathrm{~kg}\) and \(M \mathrm{~kg}\) are situated at \((2,1,1),(1,2,1),(2,-2,1)\) and \((-1,4,3)\).If their center of mass is situated at ( \(1,1,3 / 2\) ), the value of \(M\) is

1 \(1 \mathrm{~kg}\)
2 \(2 \mathrm{~kg}\)
3 \(1.5 \mathrm{~kg}\)
4 \(3 \mathrm{~kg}\)
Rotational Motion

269549 Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length ' \(L\) '. If the masses of any two adjacent particles are doubled. The shift in the centre of mass is

1 \(\frac{L}{8}\)
2 \(\frac{\sqrt{3} L}{8}\)
3 \(\frac{3 L}{16}\)
4 \(\frac{3 L}{4}\)
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Rotational Motion

269546 Three identical particles each of mass \(0.1 \mathrm{~kg}\) are arranged at three corners of a square of side \(\sqrt{2} \mathrm{~m}\). The distance of the center of mass from the fourth corner is

1 \(2 / 3 \mathrm{~m}\)
2 \(4 / 3 \mathrm{~m}\)
3 \(1 \mathrm{~m}\)
4 \(8 / 3 \mathrm{~m}\)
Rotational Motion

269547 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 \(x=60 \mathrm{~cm}\) and another is at \(x=40 \mathrm{~cm}, y=60 \mathrm{~cm}\). The position of the third piece is

1 \(x=-100 \mathrm{~cm}, y=-60 \mathrm{~cm}\)
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

269548 Masses \(1 \mathrm{~kg}, 1.5 \mathrm{~kg}, 2 \mathrm{~kg}\) and \(M \mathrm{~kg}\) are situated at \((2,1,1),(1,2,1),(2,-2,1)\) and \((-1,4,3)\).If their center of mass is situated at ( \(1,1,3 / 2\) ), the value of \(M\) is

1 \(1 \mathrm{~kg}\)
2 \(2 \mathrm{~kg}\)
3 \(1.5 \mathrm{~kg}\)
4 \(3 \mathrm{~kg}\)
Rotational Motion

269549 Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length ' \(L\) '. If the masses of any two adjacent particles are doubled. The shift in the centre of mass is

1 \(\frac{L}{8}\)
2 \(\frac{\sqrt{3} L}{8}\)
3 \(\frac{3 L}{16}\)
4 \(\frac{3 L}{4}\)