Consider the two statements related to circular motion in usual notations:
$A$. In uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.
$B$. In non-uniform circular motion,$\vec{\omega}$,$\vec{v}$,and $\vec{a}$ are always mutually perpendicular.

$A$ particle moves in a plane along an elliptic path given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. At point $(0, b)$,the $x$-component of velocity is $u$. The $y$-component of acceleration at this point is

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as a function of $\phi$ can be represented as:

$A$ particle is projected from the ground with some initial velocity making an angle of $45^{\circ}$ with the horizontal. If it reaches a height of $7.5 \ m$ above the ground, while it travels a horizontal distance of $10 \ m$ from the point of projection, then the initial speed of the particle is (assume, $g=10 \ m/s^2$): (in $m/s$)

$A$ stone of mass $0.25 \; kg$ is tied to the end of a string and is being whirled in a horizontal circle of radius $1.5 \; m$ with a speed of $40 \; rev./min$. If the speed of the stone is increased beyond the maximum permissible value and the string breaks suddenly,which of the following correctly describes the trajectory of the stone after the string breaks?
$(a)$ The stone moves radially outward.
$(b)$ The stone flies off tangentially from the instant the string breaks.
$(c)$ The stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle.

$A$ particle moving in the $xy$ plane experiences a velocity-dependent force $\overrightarrow{F} = k(v_y \hat{i} + v_x \hat{j})$,where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\overrightarrow{v}$. If $\overrightarrow{a}$ is the acceleration of the particle,then which of the following statements is true for the particle?