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 V0 and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 6 m V02
2 12 m V02
3 2 m V02
4 8 m V02
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, the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity =10 ms2 )

1 10 ms2 vertically downward
2 10 ms2 vertically upward
3 5 ms2 vertically downward
4 5 ms2 vertically upward
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)
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 V0 and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 6 m V02
2 12 m V02
3 2 m V02
4 8 m V02
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, the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity =10 ms2 )

1 10 ms2 vertically downward
2 10 ms2 vertically upward
3 5 ms2 vertically downward
4 5 ms2 vertically upward
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)
Rotational Motion

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

1 i^+j^
2 12(i^+j^)
3 (i^j^)
4 12(i^j^)
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 V0 and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 6 m V02
2 12 m V02
3 2 m V02
4 8 m V02
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, the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity =10 ms2 )

1 10 ms2 vertically downward
2 10 ms2 vertically upward
3 5 ms2 vertically downward
4 5 ms2 vertically upward
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)
Rotational Motion

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

1 i^+j^
2 12(i^+j^)
3 (i^j^)
4 12(i^j^)
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 V0 and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure is

1 6 m V02
2 12 m V02
3 2 m V02
4 8 m V02
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, the acceleration of the centre of mass of the system of the two blocks is (Acceleration due to gravity =10 ms2 )

1 10 ms2 vertically downward
2 10 ms2 vertically upward
3 5 ms2 vertically downward
4 5 ms2 vertically upward
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)
Rotational Motion

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

1 i^+j^
2 12(i^+j^)
3 (i^j^)
4 12(i^j^)