00. Centre of Mass
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Rotational Motion

149762 Three particles are attached to a ring of mass \(m\) and radius \(R\) as shown in the figure. The centre of mass the ring has a speed \(V_{0}\) and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 \(6 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
2 \(12 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
3 \(2 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
4 \(8 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
AP EAMCET(Medical)-2016
Rotational Motion

149763 Two blocks of equals mass are released on two smooth sides of a double inclined plane with a fixed base as shown in the figure. If each angle of inclination is \(45^{\circ}\), the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity \(=10 \mathbf{~ m s}^{-2}\) )

1 \(10 \mathrm{~ms}^{-2}\) vertically downward
2 \(10 \mathrm{~ms}^{-2}\) vertically upward
3 \(5 \mathrm{~ms}^{-2}\) vertically downward
4 \(5 \mathrm{~ms}^{-2}\) vertically upward
AP EAMCET(Medical)-2016
Rotational Motion

149764 Match the following
| List A | List B |
| :--- | :--- |
| (i) Position of centre mass | (v) is zero |
| (ii) The algebraic sum of moments of all the masses about CM | (vi) is non-uniform gravitational field|
| (iii) CM and centre of gravity coincide |(vii) is in dependent of frame of reference|
| (iv) CM and centre of gravity do not coincide|(viii) in uniformgravitational field |
The correct match is

1 (i)-(v), (ii)-(vii), (iii)-(vi), (iv)-(viii)
2 (i)-(vii), (ii)-(v), (iii)-(vi), (iv)-(viii)
3 (i)-(vii), (ii)-(v), (iii)-(viii), (iv)-(vi)
4 (i)-(viii), (ii)-(v), (iii)-(vi), (iv)-(vii)
AP EMCET(Medical)-2011
Rotational Motion

149765 Four particles, each of mass \(1 \mathrm{~kg}\) are placed at the corners of a square \(O A B C\) of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin the co-ordinate system. \(\mathrm{OA}\) and \(O C\) are aligned along positive \(X\)-axis and positive \(\mathrm{Y}\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) '):

1 \(\hat{i}+\hat{j}\)
2 \(\frac{1}{2}(\hat{\mathrm{i}}+\hat{\mathrm{j}})\)
3 \((\hat{i}-\hat{j})\)
4 \(\frac{1}{2}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
AP EAMCET(Medical)-2006
NEET DIGITAL LIBRARY
Rotational Motion

149762 Three particles are attached to a ring of mass \(m\) and radius \(R\) as shown in the figure. The centre of mass the ring has a speed \(V_{0}\) and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 \(6 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
2 \(12 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
3 \(2 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
4 \(8 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
AP EAMCET(Medical)-2016
Rotational Motion

149763 Two blocks of equals mass are released on two smooth sides of a double inclined plane with a fixed base as shown in the figure. If each angle of inclination is \(45^{\circ}\), the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity \(=10 \mathbf{~ m s}^{-2}\) )

1 \(10 \mathrm{~ms}^{-2}\) vertically downward
2 \(10 \mathrm{~ms}^{-2}\) vertically upward
3 \(5 \mathrm{~ms}^{-2}\) vertically downward
4 \(5 \mathrm{~ms}^{-2}\) vertically upward
AP EAMCET(Medical)-2016
Rotational Motion

149764 Match the following
| List A | List B |
| :--- | :--- |
| (i) Position of centre mass | (v) is zero |
| (ii) The algebraic sum of moments of all the masses about CM | (vi) is non-uniform gravitational field|
| (iii) CM and centre of gravity coincide |(vii) is in dependent of frame of reference|
| (iv) CM and centre of gravity do not coincide|(viii) in uniformgravitational field |
The correct match is

1 (i)-(v), (ii)-(vii), (iii)-(vi), (iv)-(viii)
2 (i)-(vii), (ii)-(v), (iii)-(vi), (iv)-(viii)
3 (i)-(vii), (ii)-(v), (iii)-(viii), (iv)-(vi)
4 (i)-(viii), (ii)-(v), (iii)-(vi), (iv)-(vii)
AP EMCET(Medical)-2011
Rotational Motion

149765 Four particles, each of mass \(1 \mathrm{~kg}\) are placed at the corners of a square \(O A B C\) of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin the co-ordinate system. \(\mathrm{OA}\) and \(O C\) are aligned along positive \(X\)-axis and positive \(\mathrm{Y}\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) '):

1 \(\hat{i}+\hat{j}\)
2 \(\frac{1}{2}(\hat{\mathrm{i}}+\hat{\mathrm{j}})\)
3 \((\hat{i}-\hat{j})\)
4 \(\frac{1}{2}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
AP EAMCET(Medical)-2006
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Rotational Motion

149762 Three particles are attached to a ring of mass \(m\) and radius \(R\) as shown in the figure. The centre of mass the ring has a speed \(V_{0}\) and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 \(6 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
2 \(12 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
3 \(2 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
4 \(8 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
AP EAMCET(Medical)-2016
Rotational Motion

149763 Two blocks of equals mass are released on two smooth sides of a double inclined plane with a fixed base as shown in the figure. If each angle of inclination is \(45^{\circ}\), the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity \(=10 \mathbf{~ m s}^{-2}\) )

1 \(10 \mathrm{~ms}^{-2}\) vertically downward
2 \(10 \mathrm{~ms}^{-2}\) vertically upward
3 \(5 \mathrm{~ms}^{-2}\) vertically downward
4 \(5 \mathrm{~ms}^{-2}\) vertically upward
AP EAMCET(Medical)-2016
Rotational Motion

149764 Match the following
| List A | List B |
| :--- | :--- |
| (i) Position of centre mass | (v) is zero |
| (ii) The algebraic sum of moments of all the masses about CM | (vi) is non-uniform gravitational field|
| (iii) CM and centre of gravity coincide |(vii) is in dependent of frame of reference|
| (iv) CM and centre of gravity do not coincide|(viii) in uniformgravitational field |
The correct match is

1 (i)-(v), (ii)-(vii), (iii)-(vi), (iv)-(viii)
2 (i)-(vii), (ii)-(v), (iii)-(vi), (iv)-(viii)
3 (i)-(vii), (ii)-(v), (iii)-(viii), (iv)-(vi)
4 (i)-(viii), (ii)-(v), (iii)-(vi), (iv)-(vii)
AP EMCET(Medical)-2011
Rotational Motion

149765 Four particles, each of mass \(1 \mathrm{~kg}\) are placed at the corners of a square \(O A B C\) of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin the co-ordinate system. \(\mathrm{OA}\) and \(O C\) are aligned along positive \(X\)-axis and positive \(\mathrm{Y}\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) '):

1 \(\hat{i}+\hat{j}\)
2 \(\frac{1}{2}(\hat{\mathrm{i}}+\hat{\mathrm{j}})\)
3 \((\hat{i}-\hat{j})\)
4 \(\frac{1}{2}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
AP EAMCET(Medical)-2006
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Rotational Motion

149762 Three particles are attached to a ring of mass \(m\) and radius \(R\) as shown in the figure. The centre of mass the ring has a speed \(V_{0}\) and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 \(6 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
2 \(12 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
3 \(2 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
4 \(8 \mathrm{~m} \mathrm{~V}_{0}^{2}\)
AP EAMCET(Medical)-2016
Rotational Motion

149763 Two blocks of equals mass are released on two smooth sides of a double inclined plane with a fixed base as shown in the figure. If each angle of inclination is \(45^{\circ}\), the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity \(=10 \mathbf{~ m s}^{-2}\) )

1 \(10 \mathrm{~ms}^{-2}\) vertically downward
2 \(10 \mathrm{~ms}^{-2}\) vertically upward
3 \(5 \mathrm{~ms}^{-2}\) vertically downward
4 \(5 \mathrm{~ms}^{-2}\) vertically upward
AP EAMCET(Medical)-2016
Rotational Motion

149764 Match the following
| List A | List B |
| :--- | :--- |
| (i) Position of centre mass | (v) is zero |
| (ii) The algebraic sum of moments of all the masses about CM | (vi) is non-uniform gravitational field|
| (iii) CM and centre of gravity coincide |(vii) is in dependent of frame of reference|
| (iv) CM and centre of gravity do not coincide|(viii) in uniformgravitational field |
The correct match is

1 (i)-(v), (ii)-(vii), (iii)-(vi), (iv)-(viii)
2 (i)-(vii), (ii)-(v), (iii)-(vi), (iv)-(viii)
3 (i)-(vii), (ii)-(v), (iii)-(viii), (iv)-(vi)
4 (i)-(viii), (ii)-(v), (iii)-(vi), (iv)-(vii)
AP EMCET(Medical)-2011
Rotational Motion

149765 Four particles, each of mass \(1 \mathrm{~kg}\) are placed at the corners of a square \(O A B C\) of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin the co-ordinate system. \(\mathrm{OA}\) and \(O C\) are aligned along positive \(X\)-axis and positive \(\mathrm{Y}\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) '):

1 \(\hat{i}+\hat{j}\)
2 \(\frac{1}{2}(\hat{\mathrm{i}}+\hat{\mathrm{j}})\)
3 \((\hat{i}-\hat{j})\)
4 \(\frac{1}{2}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
AP EAMCET(Medical)-2006