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5
MCQ (Single Correct Answer)

A uniform square plate has a small piece $Q$ of an irregular shape removed and glued to the centre of the plate leaving a hole behind in figure. The moment of inertia about the $z$-axis is then,

A
increased
B
decreased
C
the same
D
changed in unpredicted manner
6
MCQ (Single Correct Answer)

In problem 5, the CM of the plate is now in the following quadrant of x-y plane.

A
I
B
II
C
III
D
IV
7
MCQ (Single Correct Answer)

The density of a non-uniform rod of length 1 m is given by $$\rho(x)=a\left(1+b x^2\right)$$ where, a and b are constants and $$0 \leq x \leq 1$$. The centre of mass of the rod will be at

A
$$\frac{3(2+b)}{4(3+b)}$$
B
$$\frac{4(2+b)}{3(3+b)}$$
C
$$\frac{3(3+b)}{4(2+b)}$$
D
$$\frac{4(3+b)}{3(2+b)}$$
8
MCQ (Single Correct Answer)

A merry-go-round, made of a ring-like platform of radius $$R$$ and mass $$M$$, is revolving with angular speed $$\omega$$. A person of mass $$M$$ is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round of afterwards is

A
$$2 \omega$$
B
$$\omega$$
C
$$\frac{\omega}{2}$$
D
0
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.
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