QBManager

Rotational Motion

269432 Two objects of masses $200 g$ and $500 g$ have velocities of $10 i m / s$ and $(3 i + 5 j) m / s$ respectively. The velocity of their centre of mass is

1

5 i - 25 j

2

\frac{5}{7} i - 25 j

3

5 i + \frac{25}{7} j

4

25 i - \frac{5}{7} j

Explanation:

${\vec{v}}_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}}$

Rotational Motion

269497 Two particles of masses" $p$ " and " $q$ " ( $p < q$ ) are separated by a distance "d". The shift in the centre of mass when the two particles are interchanged is

1

d (p + q) / (p - q)

2

d (p - q) / (p + q)

3

d p / (p - q)

4

d q / (p - q)

Explanation:

$x_{c m} = \frac{m_{2} d}{m_{1} + m_{2}} = \frac{p d}{p + q}$
$x_{c m}^{1} = \frac{m_{1} d}{m_{1} + m_{2}} = \frac{q d}{p + q}; shift = x_{c m}^{1} \sim x_{c m}$

Rotational Motion

269496 Two particles of equal masses have velocities ${\vec{v}}_{1} = 4 \hat{i}$ and ${\vec{v}}_{2} = 4 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {m s}^{- 2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

1 Straight line

2 Parabola

3 Circle

4 Ellipse

Explanation:

$\vec{V_{c m}}$ parallel to $\vec{a_{c m}}$

Rotational Motion

269553 Two particles of equal mass have velocities ${\vec{V}}_{1} = 8 \hat{i}$ and ${\vec{V}}_{2} = 8 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {ms}^{- 2}$ while the acceleration of the other particle is zero.The centre of mass of the two particles moves is a path of

1 straight line

2 parabola

3 circle

4 ellipse

Explanation:

$v_{c m}$ is parallel to $a_{c m}$

Rotational Motion

269592 Seven homogeneous bricks each of length L,mass $M$ are arranged as shown. Projection $x = \frac{L}{10}$ then $x$ co-ordinate of C.M is

1

\frac{22}{35} L

2

\frac{32}{35} L

3

\frac{42}{35} L

4

\frac{12}{35} L

Explanation:

$x_{c m} = \frac{\sum m_{i} x_{i}}{\sum m_{i}}$

Rotational Motion

269432 Two objects of masses $200 g$ and $500 g$ have velocities of $10 i m / s$ and $(3 i + 5 j) m / s$ respectively. The velocity of their centre of mass is

1

5 i - 25 j

2

\frac{5}{7} i - 25 j

3

5 i + \frac{25}{7} j

4

25 i - \frac{5}{7} j

Explanation:

${\vec{v}}_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}}$

Rotational Motion

269497 Two particles of masses" $p$ " and " $q$ " ( $p < q$ ) are separated by a distance "d". The shift in the centre of mass when the two particles are interchanged is

1

d (p + q) / (p - q)

2

d (p - q) / (p + q)

3

d p / (p - q)

4

d q / (p - q)

Explanation:

$x_{c m} = \frac{m_{2} d}{m_{1} + m_{2}} = \frac{p d}{p + q}$
$x_{c m}^{1} = \frac{m_{1} d}{m_{1} + m_{2}} = \frac{q d}{p + q}; shift = x_{c m}^{1} \sim x_{c m}$

Rotational Motion

269496 Two particles of equal masses have velocities ${\vec{v}}_{1} = 4 \hat{i}$ and ${\vec{v}}_{2} = 4 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {m s}^{- 2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

1 Straight line

2 Parabola

3 Circle

4 Ellipse

Explanation:

$\vec{V_{c m}}$ parallel to $\vec{a_{c m}}$

Rotational Motion

269553 Two particles of equal mass have velocities ${\vec{V}}_{1} = 8 \hat{i}$ and ${\vec{V}}_{2} = 8 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {ms}^{- 2}$ while the acceleration of the other particle is zero.The centre of mass of the two particles moves is a path of

1 straight line

2 parabola

3 circle

4 ellipse

Explanation:

$v_{c m}$ is parallel to $a_{c m}$

Rotational Motion

269592 Seven homogeneous bricks each of length L,mass $M$ are arranged as shown. Projection $x = \frac{L}{10}$ then $x$ co-ordinate of C.M is

1

\frac{22}{35} L

2

\frac{32}{35} L

3

\frac{42}{35} L

4

\frac{12}{35} L

Explanation:

$x_{c m} = \frac{\sum m_{i} x_{i}}{\sum m_{i}}$

Rotational Motion

269432 Two objects of masses $200 g$ and $500 g$ have velocities of $10 i m / s$ and $(3 i + 5 j) m / s$ respectively. The velocity of their centre of mass is

1

5 i - 25 j

2

\frac{5}{7} i - 25 j

3

5 i + \frac{25}{7} j

4

25 i - \frac{5}{7} j

Explanation:

${\vec{v}}_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}}$

Rotational Motion

269497 Two particles of masses" $p$ " and " $q$ " ( $p < q$ ) are separated by a distance "d". The shift in the centre of mass when the two particles are interchanged is

1

d (p + q) / (p - q)

2

d (p - q) / (p + q)

3

d p / (p - q)

4

d q / (p - q)

Explanation:

$x_{c m} = \frac{m_{2} d}{m_{1} + m_{2}} = \frac{p d}{p + q}$
$x_{c m}^{1} = \frac{m_{1} d}{m_{1} + m_{2}} = \frac{q d}{p + q}; shift = x_{c m}^{1} \sim x_{c m}$

Rotational Motion

269496 Two particles of equal masses have velocities ${\vec{v}}_{1} = 4 \hat{i}$ and ${\vec{v}}_{2} = 4 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {m s}^{- 2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

1 Straight line

2 Parabola

3 Circle

4 Ellipse

Explanation:

$\vec{V_{c m}}$ parallel to $\vec{a_{c m}}$

Rotational Motion

269553 Two particles of equal mass have velocities ${\vec{V}}_{1} = 8 \hat{i}$ and ${\vec{V}}_{2} = 8 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {ms}^{- 2}$ while the acceleration of the other particle is zero.The centre of mass of the two particles moves is a path of

1 straight line

2 parabola

3 circle

4 ellipse

Explanation:

$v_{c m}$ is parallel to $a_{c m}$

Rotational Motion

269592 Seven homogeneous bricks each of length L,mass $M$ are arranged as shown. Projection $x = \frac{L}{10}$ then $x$ co-ordinate of C.M is

1

\frac{22}{35} L

2

\frac{32}{35} L

3

\frac{42}{35} L

4

\frac{12}{35} L

Explanation:

$x_{c m} = \frac{\sum m_{i} x_{i}}{\sum m_{i}}$

Rotational Motion

269432 Two objects of masses $200 g$ and $500 g$ have velocities of $10 i m / s$ and $(3 i + 5 j) m / s$ respectively. The velocity of their centre of mass is

1

5 i - 25 j

2

\frac{5}{7} i - 25 j

3

5 i + \frac{25}{7} j

4

25 i - \frac{5}{7} j

Explanation:

${\vec{v}}_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}}$

Rotational Motion

269497 Two particles of masses" $p$ " and " $q$ " ( $p < q$ ) are separated by a distance "d". The shift in the centre of mass when the two particles are interchanged is

1

d (p + q) / (p - q)

2

d (p - q) / (p + q)

3

d p / (p - q)

4

d q / (p - q)

Explanation:

$x_{c m} = \frac{m_{2} d}{m_{1} + m_{2}} = \frac{p d}{p + q}$
$x_{c m}^{1} = \frac{m_{1} d}{m_{1} + m_{2}} = \frac{q d}{p + q}; shift = x_{c m}^{1} \sim x_{c m}$

Rotational Motion

269496 Two particles of equal masses have velocities ${\vec{v}}_{1} = 4 \hat{i}$ and ${\vec{v}}_{2} = 4 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {m s}^{- 2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

1 Straight line

2 Parabola

3 Circle

4 Ellipse

Explanation:

$\vec{V_{c m}}$ parallel to $\vec{a_{c m}}$

Rotational Motion

269553 Two particles of equal mass have velocities ${\vec{V}}_{1} = 8 \hat{i}$ and ${\vec{V}}_{2} = 8 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {ms}^{- 2}$ while the acceleration of the other particle is zero.The centre of mass of the two particles moves is a path of

1 straight line

2 parabola

3 circle

4 ellipse

Explanation:

$v_{c m}$ is parallel to $a_{c m}$

Rotational Motion

269592 Seven homogeneous bricks each of length L,mass $M$ are arranged as shown. Projection $x = \frac{L}{10}$ then $x$ co-ordinate of C.M is

1

\frac{22}{35} L

2

\frac{32}{35} L

3

\frac{42}{35} L

4

\frac{12}{35} L

Explanation:

$x_{c m} = \frac{\sum m_{i} x_{i}}{\sum m_{i}}$

Rotational Motion

269432 Two objects of masses $200 g$ and $500 g$ have velocities of $10 i m / s$ and $(3 i + 5 j) m / s$ respectively. The velocity of their centre of mass is

1

5 i - 25 j

2

\frac{5}{7} i - 25 j

3

5 i + \frac{25}{7} j

4

25 i - \frac{5}{7} j

Explanation:

${\vec{v}}_{c m} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}}$

Rotational Motion

269497 Two particles of masses" $p$ " and " $q$ " ( $p < q$ ) are separated by a distance "d". The shift in the centre of mass when the two particles are interchanged is

1

d (p + q) / (p - q)

2

d (p - q) / (p + q)

3

d p / (p - q)

4

d q / (p - q)

Explanation:

$x_{c m} = \frac{m_{2} d}{m_{1} + m_{2}} = \frac{p d}{p + q}$
$x_{c m}^{1} = \frac{m_{1} d}{m_{1} + m_{2}} = \frac{q d}{p + q}; shift = x_{c m}^{1} \sim x_{c m}$

Rotational Motion

269496 Two particles of equal masses have velocities ${\vec{v}}_{1} = 4 \hat{i}$ and ${\vec{v}}_{2} = 4 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {m s}^{- 2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

1 Straight line

2 Parabola

3 Circle

4 Ellipse

Explanation:

$\vec{V_{c m}}$ parallel to $\vec{a_{c m}}$

Rotational Motion

269553 Two particles of equal mass have velocities ${\vec{V}}_{1} = 8 \hat{i}$ and ${\vec{V}}_{2} = 8 \hat{j}$ . First particle has an acceleration ${\vec{a}}_{1} = (5 \hat{i} + 5 \hat{j}) {ms}^{- 2}$ while the acceleration of the other particle is zero.The centre of mass of the two particles moves is a path of

1 straight line

2 parabola

3 circle

4 ellipse

Explanation:

$v_{c m}$ is parallel to $a_{c m}$

Rotational Motion

269592 Seven homogeneous bricks each of length L,mass $M$ are arranged as shown. Projection $x = \frac{L}{10}$ then $x$ co-ordinate of C.M is

1

\frac{22}{35} L

2

\frac{32}{35} L

3

\frac{42}{35} L

4

\frac{12}{35} L

Explanation:

$x_{c m} = \frac{\sum m_{i} x_{i}}{\sum m_{i}}$