A particle of mass \(m\) moves with a constant velocity along \(3\) different paths, \(DE, OA\) and \(BC\). Which of the following statements is not correct about its angular momentum about point \(O\)?

                     

1.	It is zero when it is at \(A\) and moving along \(OA\).
2.	The same at all points along the line \(DE\).
3.	Of the same magnitude but oppositely directed at \(B\) and \(D\).
4.	Increases as it moves along the line \(BC\).

$\mathrm{A} \mathrm{particle} \mathrm{of} \mathrm{mass} 0.2 \mathrm{kg} \mathrm{is} \mathrm{moving} \mathrm{in} \mathrm{a} \mathrm{circle} \mathrm{of} \mathrm{radius} 1\mathrm{m} \mathrm{with}$
$\mathrm{f}=2/\mathrm{\pi } \mathrm{rps}, \mathrm{then} \mathrm{its} \mathrm{angular} \mathrm{momentum} \mathrm{is}-$
$\left(\mathrm{A}\right) 0.8 {\mathrm{kgm}}^2/\mathrm{s} \left(\mathrm{B}\right) 2 {\mathrm{kgm}}^2/\mathrm{s}$
$\left(\mathrm{C}\right) 8 {\mathrm{kgm}}^2/\mathrm{s} \left(\mathrm{D}\right) 16 {\mathrm{kgm}}^2/\mathrm{s}$

In free space, a rifle of mass \(M\) shoots a bullet of mass \(m\) at a stationary block of mass \(M\) at a distance \(D\) away from it. When the bullet has moved through a distance \(d\) towards the block, the centre of mass of the bullet-block system is at a distance of:
1. \(\frac{D-d}{M+m}~\text{from the bullet}\)
2. \(\frac{md+ MD}{M+m}~\text{from the block}\)
3. \(\frac{2md+ MD}{M+m}~\text{from the block}\)
4. \(\frac{(D-d)M}{M+m}~\text{from the bullet}\)

Blocks A and B are resting on a smooth horizontal surface given equal speeds of 2 m/s in the opposite sense as shown in the figure.

At t = 0, the position of blocks are shown, then the coordinates of centre of mass at t = 3s will be 

1.  (1, 0)

2.  (3, 0)

3.  (5, 0)

4.  (2.25, 0)

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

1. 800 rad

2. 400 rad

3. 200 rad

4. 100 rad

Moment of inertia of an object does not depend upon

A force $\overrightarrow{\mathrm{F}} = 4\hat{\mathrm{i}} - 5\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ is acting on a point $\overrightarrow{{\mathrm{r}}_1} = \hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$. The torque acting about a point $\overrightarrow{{\mathrm{r}}_2} = 3\hat{\mathrm{i}} - 2\hat{\mathrm{j}} - 3\hat{\mathrm{k}}$ is

1.  0

2.  $42\hat{\mathrm{i}} - 30\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$

2.  $42\hat{\mathrm{i}} + 30\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$

4.  $42\hat{\mathrm{i}} + 30\hat{\mathrm{j}} - 6\hat{\mathrm{k}}$

A thin uniform circular disc of mass \(M\) and radius \(R\) is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity $\omega$. Another disc of the same dimensions but of mass \(\frac{1}{4}M\) is placed gently on the first disc co-axially. The angular velocity of the system will be:

When a torque acting upon a system is zero, then which of the following will be constant