A $100 \,kg$ car is moving with a maximum velocity of $9 \,m/s$ across a circular track of radius $30\,m$. The maximum force of friction between the road and the car is ........ $N$

A block of mass $m$ is kept on horizontal turn table at $x$ distance from the centre. If coefficient of friction between block and surface of turn table is $\mu$, then maximum angular speed of the table so that block does not slip

Defined a vehicle can be parked on a slope.

A boy is sitting on the horizontal platform of a joy wheel at a distance of $5 \,m$ from the center. The wheel begins to rotate and when the angular speed exceeds $1 \,rad / s$, the boy just slips. The coefficient of friction between the boy and the wheel is $\left(g=10 \,m / s ^2\right)$

At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]

A coin placed on a rotating table just slips if it is placed at a distance $4r$ from the centre. On doubling the angular velocity of the table, the coin will just slip when at a distance from the centre equal to