A circular disc is to be made by using iron and aluminium, so that it acquires maximum moment of inertia about its geometrical axis.  It is possible with

1. iron and aluminium layers in alternate order

2. aluminium at interior and iron surrounding it

3. iron at interior and aluminium surrounding it

4. either '1' or '3'

Two Circular discs A and B are of equal masses and thicknesses but made of metal with densities ${\mathrm{d}}_{\mathrm{A}} \mathrm{and} {\mathrm{d}}_{\mathrm{B}}$ (${\mathrm{d}}_{\mathrm{A}} > {\mathrm{d}}_{\mathrm{B}}$). If their moments of inertia about an axis passing through their centers and perpendicular to circular faces be ${\mathrm{I}}_{\mathrm{A}} \mathrm{and} {\mathrm{I}}_{\mathrm{B}}$, then

1.  ${\mathrm{I}}_{\mathrm{A}} = {\mathrm{I}}_{\mathrm{B}}$

2.  ${\mathrm{I}}_{\mathrm{A}} > {\mathrm{I}}_{\mathrm{B}}$

3.  ${\mathrm{I}}_{\mathrm{A}}\hspace{0.17em}<\hspace{0.17em}{\mathrm{I}}_{\mathrm{B}}$

4.  ${\mathrm{I}}_{\mathrm{A}} \ge {\mathrm{I}}_{\mathrm{B}}$

A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to the translational kinetic energy. The body is 

1.  Disc

2.  Sphere

3.  Cylinder

4.  Ring

A wheel with a radius of \(20\) cm has forces applied to it as shown in the figure. The torque produced by the forces of \(4\) N at \(A\), \(8~\)N at \(B\), \(6\) N at \(C\), and \(9~\)N at \(D\), at the angles indicated, is:

1. \(5.4\) N-m anticlockwise

2. \(1.80\) N-m clockwise

3. \(2.0\) N-m clockwise

4. \(3.6\) N-m clockwise

The moment of inertia of a thin rectangular plate \(\text {ABCD}\) of uniform thickness about an axis passing through the centre \(\text O\) and perpendicular to the plane of the plate is 

1.  \(\text I_{1}   +   \text I_{2}\)

2.  \(\text I_{2}   +  \text I_{4}\)

3.  \(\text I_{1}   - \text   I_{3}\)

4.  \(\text I_{1}   +\text   I_{2  } +  \text I_{3}   + \text   I_{4}\)

The centre of a wheel rolling on a plane surface moves with a speed \(v_0.\) A particle on the rim of the wheel at the same level as the centre will be moving at speed:
1. zero
2. \(v_0\)
3. \(\sqrt{2}v_0\)
4. \(2v_0\)

Moment of inertia of a uniform cylinder of mass M, radius R and length l about an axis passing through its center and normal to its axis would be

1.  $\frac{{\mathrm{Ml}}^2}{12}$

2.  $\frac{{\mathrm{MR}}^2}{2}$

3.  $\mathrm{M}\left[\frac{{\mathrm{l}}^2}{12} + \frac{{\mathrm{R}}^2}{4}\right]$

4.  $\mathrm{M}\left[\frac{{\mathrm{l}}^2}{12} + \frac{{\mathrm{R}}^2}{2}\right]$

A particle moves along a circle of radius $\frac{20}{\mathrm{\pi }}m$ with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begin, the tangential acceleration is

1. 640 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

2. 160 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

3. 40 $\mathrm{\pi } \mathrm{m}/{\mathrm{s}}^2$

4. 40 $\mathrm{m}/{\mathrm{s}}^2$

If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:

A wheel has angular acceleration of 3.0 rad/$se{c}^2$ and an initial angular speed of 2.00 rad/sec.  In a time of 2 sec it has rotated through an angle (in radian) of 

1. 10               

2. 12

3. 4                 

4. 6