00. Centre of Mass
Rotational Motion

269426 Particles of masses\(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are at \((2 i+5 j+13 k) m\) and \((-6 i+4 j-2 k) m\) then instantaneous position of their centre of mass is

1 \(\frac{1}{4}(-16 i+17 j+7 k) m\)
2 \(\frac{1}{4}(-8 i+17 j+7 k) m\)
3 \(\frac{1}{4}(-6 i+17 j+7 k) m\)
4 \(\frac{1}{4}(-6 i+17 j+5 k) m\)
Rotational Motion

269427 A boat of mass\(50 \mathrm{~kg}\) is at rest. A dog of mass \(5 \mathrm{~kg}\) moves in the boat with a velocity of \(20 \mathrm{~m} /\) \(\mathrm{s}\). What is the velocity of boat?

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

269481 A uniform wire is bent into the form of a rectangle of length\(L\) and width \(W\). The coordinates of its centre of mass from a corner are

1 \((0,0)\)
2 \(\square \frac{L}{2}, \mathrm{w} E\)
3 \(\mathrm{f}, \frac{W}{2}\) -
4 \(\mathrm{A}^{L}, \frac{W}{2} \cdot\)
Rotational Motion

269482 A uniform disc of radius\(R\) is put over another uniform disc of radius \(2 R\) of same thickness and density. The peripheries of the two discs touch each other. The position of their centre of mass is

1 at \(R / 3\) from thecentre of the bigger disc towards the centre of the smaller disc
2 at \(R / 5\) from thecentre of the bigger disc towards the centre of the smaller disc
3 at\(2 R / 5\) from the centre of the bigger disc towards the centre of the smaller disc
4 at\(2 R / 5\) from the centre of the smaller disc
Rotational Motion

269483 Three particles each \(1 \mathrm{~kg}\) mass are placed at the corners of a right angled triangle AOB, \(O\) being the origin of the co-ordinate system \(\mathrm{OA}\) and \(\mathrm{OB}\) along +ve \(x\)-direction and +ve \(y-\) direction. The position vector of the centre of mass is \((O A=O B=1 \mathrm{~m}) \quad\) (in meters)

1 \(\frac{i+j}{3}\)
2 \(\frac{i-j}{3}\)
3 \(\frac{2(i+j)}{3}\)
4 \((i-j)\)
Rotational Motion

269426 Particles of masses\(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are at \((2 i+5 j+13 k) m\) and \((-6 i+4 j-2 k) m\) then instantaneous position of their centre of mass is

1 \(\frac{1}{4}(-16 i+17 j+7 k) m\)
2 \(\frac{1}{4}(-8 i+17 j+7 k) m\)
3 \(\frac{1}{4}(-6 i+17 j+7 k) m\)
4 \(\frac{1}{4}(-6 i+17 j+5 k) m\)
Rotational Motion

269427 A boat of mass\(50 \mathrm{~kg}\) is at rest. A dog of mass \(5 \mathrm{~kg}\) moves in the boat with a velocity of \(20 \mathrm{~m} /\) \(\mathrm{s}\). What is the velocity of boat?

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

269481 A uniform wire is bent into the form of a rectangle of length\(L\) and width \(W\). The coordinates of its centre of mass from a corner are

1 \((0,0)\)
2 \(\square \frac{L}{2}, \mathrm{w} E\)
3 \(\mathrm{f}, \frac{W}{2}\) -
4 \(\mathrm{A}^{L}, \frac{W}{2} \cdot\)
Rotational Motion

269482 A uniform disc of radius\(R\) is put over another uniform disc of radius \(2 R\) of same thickness and density. The peripheries of the two discs touch each other. The position of their centre of mass is

1 at \(R / 3\) from thecentre of the bigger disc towards the centre of the smaller disc
2 at \(R / 5\) from thecentre of the bigger disc towards the centre of the smaller disc
3 at\(2 R / 5\) from the centre of the bigger disc towards the centre of the smaller disc
4 at\(2 R / 5\) from the centre of the smaller disc
Rotational Motion

269483 Three particles each \(1 \mathrm{~kg}\) mass are placed at the corners of a right angled triangle AOB, \(O\) being the origin of the co-ordinate system \(\mathrm{OA}\) and \(\mathrm{OB}\) along +ve \(x\)-direction and +ve \(y-\) direction. The position vector of the centre of mass is \((O A=O B=1 \mathrm{~m}) \quad\) (in meters)

1 \(\frac{i+j}{3}\)
2 \(\frac{i-j}{3}\)
3 \(\frac{2(i+j)}{3}\)
4 \((i-j)\)
Rotational Motion

269426 Particles of masses\(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are at \((2 i+5 j+13 k) m\) and \((-6 i+4 j-2 k) m\) then instantaneous position of their centre of mass is

1 \(\frac{1}{4}(-16 i+17 j+7 k) m\)
2 \(\frac{1}{4}(-8 i+17 j+7 k) m\)
3 \(\frac{1}{4}(-6 i+17 j+7 k) m\)
4 \(\frac{1}{4}(-6 i+17 j+5 k) m\)
Rotational Motion

269427 A boat of mass\(50 \mathrm{~kg}\) is at rest. A dog of mass \(5 \mathrm{~kg}\) moves in the boat with a velocity of \(20 \mathrm{~m} /\) \(\mathrm{s}\). What is the velocity of boat?

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

269481 A uniform wire is bent into the form of a rectangle of length\(L\) and width \(W\). The coordinates of its centre of mass from a corner are

1 \((0,0)\)
2 \(\square \frac{L}{2}, \mathrm{w} E\)
3 \(\mathrm{f}, \frac{W}{2}\) -
4 \(\mathrm{A}^{L}, \frac{W}{2} \cdot\)
Rotational Motion

269482 A uniform disc of radius\(R\) is put over another uniform disc of radius \(2 R\) of same thickness and density. The peripheries of the two discs touch each other. The position of their centre of mass is

1 at \(R / 3\) from thecentre of the bigger disc towards the centre of the smaller disc
2 at \(R / 5\) from thecentre of the bigger disc towards the centre of the smaller disc
3 at\(2 R / 5\) from the centre of the bigger disc towards the centre of the smaller disc
4 at\(2 R / 5\) from the centre of the smaller disc
Rotational Motion

269483 Three particles each \(1 \mathrm{~kg}\) mass are placed at the corners of a right angled triangle AOB, \(O\) being the origin of the co-ordinate system \(\mathrm{OA}\) and \(\mathrm{OB}\) along +ve \(x\)-direction and +ve \(y-\) direction. The position vector of the centre of mass is \((O A=O B=1 \mathrm{~m}) \quad\) (in meters)

1 \(\frac{i+j}{3}\)
2 \(\frac{i-j}{3}\)
3 \(\frac{2(i+j)}{3}\)
4 \((i-j)\)
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Rotational Motion

269426 Particles of masses\(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are at \((2 i+5 j+13 k) m\) and \((-6 i+4 j-2 k) m\) then instantaneous position of their centre of mass is

1 \(\frac{1}{4}(-16 i+17 j+7 k) m\)
2 \(\frac{1}{4}(-8 i+17 j+7 k) m\)
3 \(\frac{1}{4}(-6 i+17 j+7 k) m\)
4 \(\frac{1}{4}(-6 i+17 j+5 k) m\)
Rotational Motion

269427 A boat of mass\(50 \mathrm{~kg}\) is at rest. A dog of mass \(5 \mathrm{~kg}\) moves in the boat with a velocity of \(20 \mathrm{~m} /\) \(\mathrm{s}\). What is the velocity of boat?

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

269481 A uniform wire is bent into the form of a rectangle of length\(L\) and width \(W\). The coordinates of its centre of mass from a corner are

1 \((0,0)\)
2 \(\square \frac{L}{2}, \mathrm{w} E\)
3 \(\mathrm{f}, \frac{W}{2}\) -
4 \(\mathrm{A}^{L}, \frac{W}{2} \cdot\)
Rotational Motion

269482 A uniform disc of radius\(R\) is put over another uniform disc of radius \(2 R\) of same thickness and density. The peripheries of the two discs touch each other. The position of their centre of mass is

1 at \(R / 3\) from thecentre of the bigger disc towards the centre of the smaller disc
2 at \(R / 5\) from thecentre of the bigger disc towards the centre of the smaller disc
3 at\(2 R / 5\) from the centre of the bigger disc towards the centre of the smaller disc
4 at\(2 R / 5\) from the centre of the smaller disc
Rotational Motion

269483 Three particles each \(1 \mathrm{~kg}\) mass are placed at the corners of a right angled triangle AOB, \(O\) being the origin of the co-ordinate system \(\mathrm{OA}\) and \(\mathrm{OB}\) along +ve \(x\)-direction and +ve \(y-\) direction. The position vector of the centre of mass is \((O A=O B=1 \mathrm{~m}) \quad\) (in meters)

1 \(\frac{i+j}{3}\)
2 \(\frac{i-j}{3}\)
3 \(\frac{2(i+j)}{3}\)
4 \((i-j)\)
Rotational Motion

269426 Particles of masses\(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) are at \((2 i+5 j+13 k) m\) and \((-6 i+4 j-2 k) m\) then instantaneous position of their centre of mass is

1 \(\frac{1}{4}(-16 i+17 j+7 k) m\)
2 \(\frac{1}{4}(-8 i+17 j+7 k) m\)
3 \(\frac{1}{4}(-6 i+17 j+7 k) m\)
4 \(\frac{1}{4}(-6 i+17 j+5 k) m\)
Rotational Motion

269427 A boat of mass\(50 \mathrm{~kg}\) is at rest. A dog of mass \(5 \mathrm{~kg}\) moves in the boat with a velocity of \(20 \mathrm{~m} /\) \(\mathrm{s}\). What is the velocity of boat?

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

269481 A uniform wire is bent into the form of a rectangle of length\(L\) and width \(W\). The coordinates of its centre of mass from a corner are

1 \((0,0)\)
2 \(\square \frac{L}{2}, \mathrm{w} E\)
3 \(\mathrm{f}, \frac{W}{2}\) -
4 \(\mathrm{A}^{L}, \frac{W}{2} \cdot\)
Rotational Motion

269482 A uniform disc of radius\(R\) is put over another uniform disc of radius \(2 R\) of same thickness and density. The peripheries of the two discs touch each other. The position of their centre of mass is

1 at \(R / 3\) from thecentre of the bigger disc towards the centre of the smaller disc
2 at \(R / 5\) from thecentre of the bigger disc towards the centre of the smaller disc
3 at\(2 R / 5\) from the centre of the bigger disc towards the centre of the smaller disc
4 at\(2 R / 5\) from the centre of the smaller disc
Rotational Motion

269483 Three particles each \(1 \mathrm{~kg}\) mass are placed at the corners of a right angled triangle AOB, \(O\) being the origin of the co-ordinate system \(\mathrm{OA}\) and \(\mathrm{OB}\) along +ve \(x\)-direction and +ve \(y-\) direction. The position vector of the centre of mass is \((O A=O B=1 \mathrm{~m}) \quad\) (in meters)

1 \(\frac{i+j}{3}\)
2 \(\frac{i-j}{3}\)
3 \(\frac{2(i+j)}{3}\)
4 \((i-j)\)