$A$ particle moves in a circular path of radius $R$ with an angular velocity $\omega = a - bt$,where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $t = \frac{2a}{b}$ is:

Tangential acceleration of a particle moving in a circle of radius $1 \, m$ varies with time $t$ as shown in the graph (initial velocity of the particle is zero). The time after which the total acceleration of the particle makes an angle of $30^{\circ}$ with the radial acceleration is:

$A$ particle is in uniform circular motion. The equation of its trajectory is given by $(x-2)^2+y^2=25$,where $x$ and $y$ are in meters. The speed of the particle is $2 \text{ m/s}$. When the particle attains the lowest $y$ coordinate,the acceleration of the particle is (in $\text{m/s}^2$):

The acceleration of a body in a non-uniform circular motion is $5\, ms^{-2}$. Which one of the following is correct?

In non-uniform circular motion,the ratio of tangential to radial acceleration is ($r=$ radius of the circle,$u=$ speed of the particle,$\alpha=$ angular acceleration).

$A$ body is moving along a circular track of radius $100 \ m$ with velocity $20 \ m/s$. Its tangential acceleration is $3 \ m/s^{2}$,then its resultant acceleration will be (in $m/s^{2}$)