QBManager

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365934 A rod of mass $2 m$ and $2 ℓ$ length is bent into $L$ shape at its mid point. The moment of inertia at its mid point is.

1

\frac{m ℓ^{2}}{6}

2

2 m ℓ^{2}

3

\frac{2 m ℓ^{2}}{3}

4

\frac{m ℓ^{2}}{3}

Explanation:

$I = I_{1} + I_{2}$
$= \frac{m ℓ^{2}}{3} + \frac{m ℓ^{2}}{3} = \frac{2 m ℓ^{2}}{3}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365935 A square frame $A B C D$ is formed by four identical rods each of mass $m$ and length $l$ . This frame is in $x y$ - plane such that side $A B$ coincides with $X$ - axis and side $A D$ along $Y$ - axis. The moment of inertia of the frame about $X$ - axis is

1

\frac{5 m l^{2}}{3}

2

\frac{2 m l^{2}}{3}

3

\frac{4 m l^{2}}{3}

4

\frac{m l^{2}}{12}

Explanation:

supporting img
The moment of inertia of the frame about $X$ axis,
$I = I_{A B} + I_{B C} + I_{C D} + I_{D A}$
$= 0 + \frac{m l^{2}}{3} + m l^{2} + \frac{m l^{2}}{3}$
$\Rightarrow I = \frac{5 m l^{2}}{3}$

MHTCET - 2018

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365936 Two spheres each of mass $M$ and radius $R / 2$ are connected with a mass less rod of length $2 R$ as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod
supporting img

1

\frac{21}{5} M R^{2}

2

\frac{2}{5} M R^{2}

3

\frac{5}{2} M R^{2}

4

\frac{5}{21} M R^{2}

Explanation:

$I = 2 [\frac{2}{5} M {(\frac{R}{2})}^{2}] + M (2 R)^{2} = \frac{21}{5} M R^{2}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365937 A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ . The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be
supporting img

1

\frac{M L^{2}}{12}

2

\frac{M L^{2}}{3}

3

\frac{M L^{2}}{6}

4

\frac{M L^{2}}{24}

Explanation:

Moment of inertia of a uniform rod about one end $= \frac{M l^{2}}{3}$
$∴$ Moment of inertia of the system
$= 2 \times (\frac{M}{2}) \frac{{(\frac{L}{2})}^{2}}{3} = \frac{M L^{2}}{12}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365934 A rod of mass $2 m$ and $2 ℓ$ length is bent into $L$ shape at its mid point. The moment of inertia at its mid point is.

1

\frac{m ℓ^{2}}{6}

2

2 m ℓ^{2}

3

\frac{2 m ℓ^{2}}{3}

4

\frac{m ℓ^{2}}{3}

Explanation:

$I = I_{1} + I_{2}$
$= \frac{m ℓ^{2}}{3} + \frac{m ℓ^{2}}{3} = \frac{2 m ℓ^{2}}{3}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365935 A square frame $A B C D$ is formed by four identical rods each of mass $m$ and length $l$ . This frame is in $x y$ - plane such that side $A B$ coincides with $X$ - axis and side $A D$ along $Y$ - axis. The moment of inertia of the frame about $X$ - axis is

1

\frac{5 m l^{2}}{3}

2

\frac{2 m l^{2}}{3}

3

\frac{4 m l^{2}}{3}

4

\frac{m l^{2}}{12}

Explanation:

supporting img
The moment of inertia of the frame about $X$ axis,
$I = I_{A B} + I_{B C} + I_{C D} + I_{D A}$
$= 0 + \frac{m l^{2}}{3} + m l^{2} + \frac{m l^{2}}{3}$
$\Rightarrow I = \frac{5 m l^{2}}{3}$

MHTCET - 2018

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365936 Two spheres each of mass $M$ and radius $R / 2$ are connected with a mass less rod of length $2 R$ as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod
supporting img

1

\frac{21}{5} M R^{2}

2

\frac{2}{5} M R^{2}

3

\frac{5}{2} M R^{2}

4

\frac{5}{21} M R^{2}

Explanation:

$I = 2 [\frac{2}{5} M {(\frac{R}{2})}^{2}] + M (2 R)^{2} = \frac{21}{5} M R^{2}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365937 A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ . The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be
supporting img

1

\frac{M L^{2}}{12}

2

\frac{M L^{2}}{3}

3

\frac{M L^{2}}{6}

4

\frac{M L^{2}}{24}

Explanation:

Moment of inertia of a uniform rod about one end $= \frac{M l^{2}}{3}$
$∴$ Moment of inertia of the system
$= 2 \times (\frac{M}{2}) \frac{{(\frac{L}{2})}^{2}}{3} = \frac{M L^{2}}{12}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365934 A rod of mass $2 m$ and $2 ℓ$ length is bent into $L$ shape at its mid point. The moment of inertia at its mid point is.

1

\frac{m ℓ^{2}}{6}

2

2 m ℓ^{2}

3

\frac{2 m ℓ^{2}}{3}

4

\frac{m ℓ^{2}}{3}

Explanation:

$I = I_{1} + I_{2}$
$= \frac{m ℓ^{2}}{3} + \frac{m ℓ^{2}}{3} = \frac{2 m ℓ^{2}}{3}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365935 A square frame $A B C D$ is formed by four identical rods each of mass $m$ and length $l$ . This frame is in $x y$ - plane such that side $A B$ coincides with $X$ - axis and side $A D$ along $Y$ - axis. The moment of inertia of the frame about $X$ - axis is

1

\frac{5 m l^{2}}{3}

2

\frac{2 m l^{2}}{3}

3

\frac{4 m l^{2}}{3}

4

\frac{m l^{2}}{12}

Explanation:

supporting img
The moment of inertia of the frame about $X$ axis,
$I = I_{A B} + I_{B C} + I_{C D} + I_{D A}$
$= 0 + \frac{m l^{2}}{3} + m l^{2} + \frac{m l^{2}}{3}$
$\Rightarrow I = \frac{5 m l^{2}}{3}$

MHTCET - 2018

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365936 Two spheres each of mass $M$ and radius $R / 2$ are connected with a mass less rod of length $2 R$ as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod
supporting img

1

\frac{21}{5} M R^{2}

2

\frac{2}{5} M R^{2}

3

\frac{5}{2} M R^{2}

4

\frac{5}{21} M R^{2}

Explanation:

$I = 2 [\frac{2}{5} M {(\frac{R}{2})}^{2}] + M (2 R)^{2} = \frac{21}{5} M R^{2}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365937 A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ . The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be
supporting img

1

\frac{M L^{2}}{12}

2

\frac{M L^{2}}{3}

3

\frac{M L^{2}}{6}

4

\frac{M L^{2}}{24}

Explanation:

Moment of inertia of a uniform rod about one end $= \frac{M l^{2}}{3}$
$∴$ Moment of inertia of the system
$= 2 \times (\frac{M}{2}) \frac{{(\frac{L}{2})}^{2}}{3} = \frac{M L^{2}}{12}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365934 A rod of mass $2 m$ and $2 ℓ$ length is bent into $L$ shape at its mid point. The moment of inertia at its mid point is.

1

\frac{m ℓ^{2}}{6}

2

2 m ℓ^{2}

3

\frac{2 m ℓ^{2}}{3}

4

\frac{m ℓ^{2}}{3}

Explanation:

$I = I_{1} + I_{2}$
$= \frac{m ℓ^{2}}{3} + \frac{m ℓ^{2}}{3} = \frac{2 m ℓ^{2}}{3}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365935 A square frame $A B C D$ is formed by four identical rods each of mass $m$ and length $l$ . This frame is in $x y$ - plane such that side $A B$ coincides with $X$ - axis and side $A D$ along $Y$ - axis. The moment of inertia of the frame about $X$ - axis is

1

\frac{5 m l^{2}}{3}

2

\frac{2 m l^{2}}{3}

3

\frac{4 m l^{2}}{3}

4

\frac{m l^{2}}{12}

Explanation:

supporting img
The moment of inertia of the frame about $X$ axis,
$I = I_{A B} + I_{B C} + I_{C D} + I_{D A}$
$= 0 + \frac{m l^{2}}{3} + m l^{2} + \frac{m l^{2}}{3}$
$\Rightarrow I = \frac{5 m l^{2}}{3}$

MHTCET - 2018

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365936 Two spheres each of mass $M$ and radius $R / 2$ are connected with a mass less rod of length $2 R$ as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod
supporting img

1

\frac{21}{5} M R^{2}

2

\frac{2}{5} M R^{2}

3

\frac{5}{2} M R^{2}

4

\frac{5}{21} M R^{2}

Explanation:

$I = 2 [\frac{2}{5} M {(\frac{R}{2})}^{2}] + M (2 R)^{2} = \frac{21}{5} M R^{2}$

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365937 A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $60^{\circ}$ . The moment of inertia of the rod about an axis passing through $O$ and perpendicular to the plane of the rod will be
supporting img

1

\frac{M L^{2}}{12}

2

\frac{M L^{2}}{3}

3

\frac{M L^{2}}{6}

4

\frac{M L^{2}}{24}

Explanation:

Moment of inertia of a uniform rod about one end $= \frac{M l^{2}}{3}$
$∴$ Moment of inertia of the system
$= 2 \times (\frac{M}{2}) \frac{{(\frac{L}{2})}^{2}}{3} = \frac{M L^{2}}{12}$

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Question Bank Series