A disc is rotating With an angular speed of m. If a child sits on it, which of the following is conserved? 

1.  kinetic energy 

2.  potential energy 

3.  linear momentum 

4.  angular momentum

A light cord is wrapped around the rim of the wheel disc of radius r and a steady downward pull F is exerted on the cord, then the angular acceleration of the wheel is

1. $\frac{F}{Mr}$           

2. $\frac{2F}{M}$               

3. $\frac{2F}{Mr}$               

4. $\frac{M}{2F}$

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis P is about

1.  2 kg-${\mathrm{meter}}^2$

2.  1 kg-${\mathrm{meter}}^2$

3.  0.5 kg-${\mathrm{meter}}^2$

4.  0.3 kg-${\mathrm{meter}}^2$

A particle moves in a force field given by $\overrightarrow{\mathrm{F}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\hat{\mathrm{r}}<mspace\; width="1em"></mspace>\mathrm{F}<mspace\; width="1em"></mspace>\left(\mathrm{r}\right)$, where r is the unit vector along with the position vector $\overrightarrow{\mathrm{r}}$, then which is true? 

1.  The torque acting on the particle is not zero 

2.  The torque acting on the particle produces an angular acceleration in it 

3.  The angular momentum of the particle is conserved 

4.  The angular momentum of the particle increases.

A particle of mass 5 g is moving with a uniform speed of $3\sqrt{2}$cm/s in the x-y plane along the line y = $2\sqrt{5}$cm. The magnitude of its angular momentum about the origin in $\mathrm{g}-{\mathrm{cm}}^2/\mathrm{s}$ is

1.  0

2.  30

3.  $30\sqrt{2}$

4.  $30\sqrt{10}$

Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?

A mass m is supported by a massless string wound round a uniform cylinder of mass M and radius R. On releasing the mass from rest, it will fall with an acceleration assuming no slipping-

1.  $\frac{\mathrm{g}}{3}$

2.  $\frac{\mathrm{g}}{2}$

3.  $\frac{2\mathrm{g}}{3}$

4.  g

A circular plate of diameter d is kept in contact with a square plate of an edge as shown in the figure. The density of the material and the thickness are the same everywhere. The center of mass of the composite system will be

A closed tube partly filled with water lies in a horizontal plane. If the tube is rotated about perpendicular bisector, the moment of inertia of the system

1. increases

2. decreases

3. remains constant

4. depends on sense of rotation