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

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

A particle of mass m moves along line PC with velocity v as shown.  What is the angular momentum of the particle about P?

1. mvL                 

2. mvl               

3. mvr                 

4. zero

Two bodies with moment of inertia $I_1 and I_2$ $(I_1>I_2)$ and have equal angular momenta.  If KE of rotation are $E_1 and E_2$, then

1. $E_1=E_2$             

2. $E_1>E_2$               

3.  $E_1<E_2$             

4. $E_1\ge E_2$

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

$\mathrm{}$
1. \(   \frac{PQ   +   PR   +   QR}{3}\)
2. \(  \frac{PQ   + PR}{3}\)
3. \( \frac{PQ   + QR}{3}\)
4. \(   \frac{PR   +   QR}{3}\)$\frac{\mathrm{}}{}$

Two particles of equal mass have coordinates \((2~\text{m}, 4~\text{m}, 6~\text{m})\) and \((6~\text{m},2~\text{m},8~\text{m})\). Of these one particle has velocity ${\mathrm{}}_{}$\(v_1 = 2\hat i~\text{m/s}\) and another particle has velocity \(v_2 = 2\hat j ~\text{m/s}\) at time \(t=0\). The coordinate of their centre of mass at time \(t=1~\text{s}\) will be:
1. \((4~\text{m}, 4~\text{m}, 7~\text{m})\)
2. \((5~\text{m}, 4~\text{m}, 7~\text{m})\)
3. \((2~\text{m}, 4~\text{m}, 6~\text{m})\)
4. \((4~\text{m}, 5~\text{m}, 4~\text{m})\)