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.  $30\sqrt{10}$

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 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

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 particle moves in a force field given by $\overrightarrow{\mathrm{F}} = \hat{\mathrm{r}} \mathrm{F} \left(\mathrm{r}\right)$, 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.

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 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

1.  inside the circular plate 

2.  inside the square plate

3.  at the point of contact 

4.  outside the system

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

1.  0.4 cm

2.  2.4 cm

3.  1.8 cm

4.  1.2 cm

Three indentical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

$1. \frac{\mathrm{PQ} + \mathrm{PR} + \mathrm{QR}}{3}$
$2. \frac{\mathrm{PQ} +\hspace{0.17em}\mathrm{PR}}{3}$
$3. \frac{\mathrm{PQ} +\hspace{0.17em}\mathrm{QR}}{3}$
$4. \frac{\mathrm{PR} + \mathrm{QR}}{3}$

Two particles of equal mass have coordinates (2m,4m,6m) and (6m,2m,8m). Of these one particle has velocity ${\mathrm{v}}_1=\left(2\hat{\mathrm{i}}\right)$ m/s and another particle has velocity ${\mathrm{v}}_2=\left(2\hat{j}\right)$ m/s at time t = 0. The coordinate of their centre of mass at time t = 1 s will be

1. (4m,4m,7m)

2. (5m,4m,7m)

3. (2m,4m,6m)

4. (4m,5m,4m)