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9
MCQ (Multiple Correct Answer)

Choose the correct alternatives

A
For a general rotational motion, angular momentum $$\mathbf{L}$$ and angular velocity $$\omega$$ need not be parallel.
B
For a rotational motion about a fixed axis, angular momentum $$\mathbf{L}$$ and angular velocity $$\omega$$ are always parallel.
C
For a general translational motion, momentum $$\mathbf{p}$$ and velocity $$\mathbf{v}$$ are always parallel.
D
For a general translational motion, acceleration $$\mathbf{a}$$ and velocity $$\mathbf{v}$$ are always parallel.
10
MCQ (Multiple Correct Answer)

Figure shows two identical particles 1 and 2, each of mass $$m$$, moving in opposite directions with same speed $$\mathbf{v}$$ along parallel lines. At a particular instant $$\mathbf{r}_1$$ and $$\mathbf{r}_2$$ are their respective position vectors drawn from point $$A$$ which is in the plane of the parallel lines. Choose the correct options.

A
Angular momentum $$I_1$$ of particle 1 about $$A$$ is $$I=m v\left(d_1\right)$$
B
Angular momentum $$I_2$$ of particle 2 about $$A$$ is $$I_2=\mathrm{mvr}_2$$
C
Total angular momentum of the system about $$A$$ is $$I=m v\left(\mathbf{r}_1+\mathbf{r}_2\right)$$
D
Total angular momentum of the system about $$A$$ is $$I=m v\left(d_2-d_1\right) \otimes$$
11
MCQ (Multiple Correct Answer)

The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?

A
The forces may be acting radially from a point on the axis
B
The forces may be acting on the axis of rotation
C
The forces may be acting parallel to the axis of rotation
D
The torque caused by some forces may be equal and opposite to that caused by other forces
12
MCQ (Multiple Correct Answer)

Figure shows a lamina in $$x y$$-plane. Two axes $$z$$ and $$z^{\prime}$$ pass perpendicular to its plane. A force $$\mathbf{F}$$ acts in the plane of lamina at point $$P$$ as shown. Which of the following are true? (The point $$P$$ is closer to $$z^{\prime}$$-axis than the $$z$$-axis.)

A
Torque $$\tau$$ caused by $$\mathbf{F}$$ about $$z$$-axis is along $$-\hat{\mathbf{k}}$$
B
Torque $$\tau^{\prime}$$ caused by $$\mathbf{F}$$ about $$z^{\prime}$$-axis is along $$-\hat{\mathbf{k}}$$
C
Torque $$\tau$$ caused by $$\mathbf{F}$$ about $$z$$-axis is greater in magnitude than that about $$z$$-axis
D
Total torque is given be $$\tau=\tau+\tau^{\prime}$$
13
MCQ (Multiple Correct Answer)

With reference to figure of a cube of edge $$a$$ and mass $$m$$, state whether the following are true or false. (0 is the centre of the cube.)

A
The moment of inertia of cube about z-axis is $$I_{\mathrm{z}}=I_x+I_{\mathrm{y}}$$
B
The moment of inertia of cube about $$z^{\prime}$$-axis is $$I_z=I_z+\frac{m a^2}{2}$$
C
The moment of inertia of cube about $$z^{\prime \prime}$$-axis is $$=I_z+\frac{m a^2}{2}$$
D
$$I_x=I_y$$
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