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3
MCQ (Single Correct Answer)

A particle of mass $$m$$ is moving in $$y z$$-plane with a uniform velocity $$v$$ with its trajectory running parallel to $$+v e y$$-axis and intersecting $$z$$-axis at $$z=a$$ in figure. The change in its angular momentum about the origin as it bounces elastically from a wall at $$y=$$ constant is

A
$$m v a \hat{\mathbf{e}}_x$$
B
$$2 m v a \hat{\mathbf{e}}_x$$
C
$$y m v \hat{\mathbf{e}}_x$$
D
$$2 y m v \hat{\mathbf{e}}_x$$
4
MCQ (Single Correct Answer)

When a disc rotates with uniform angular velocity, which of the following is not true?

A
The sense of rotation remains same
B
The orientation of the axis of rotation remains same
C
The speed of rotation is non-zero and remains same
D
The angular acceleration is non-zero and remains same
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
$$\frac{4(3+b)}{3(2+b)}$$
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