$A$ car is moving on a circular path of radius $500 \ m$ with a speed of $30 \ m/s$. If the speed is increasing at a rate of $2 \ m/s^2$,the net acceleration will be ......... $m/s^2$.

$A$ body of mass $2 \,kg$ moves in a horizontal circular path of radius $5 \,m$. At an instant, its speed is $2 \sqrt{5} \,m/s$ and is increasing at the rate of $3 \,m/s^2$. The magnitude of the net force acting on the body at that instant is: (in $\,N$)

In a hypothetical ring-shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has a radius of $10 \,m$, then to achieve a centripetal acceleration at a point on the circumference of $10 \,ms^{-2}$, its angular speed is:

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

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 moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of