$A$ car when passing through a convex bridge exerts a force on it which is equal to:

To mop-clean a floor,a cleaning machine presses a circular mop of radius $R$ vertically down with a total force $F$ and rotates it with a constant angular speed about its axis. If the force $F$ is distributed uniformly over the mop and the coefficient of friction between the mop and the floor is $\mu$,the torque applied by the machine on the mop is

An inextensible string of length $\ell$ fixed at one end,carries a mass $m$ at the other end. If the string makes $\frac{1}{\pi}$ revolutions per second around the vertical axis through the fixed end,the tension in the string is [The string makes an angle $\theta$ with the vertical]

If the coefficient of friction between the tires and the road is $\mu$,the maximum safe speed is $10\;m/s$. If the coefficient of friction becomes $\mu' = \frac{\mu}{2}$,what will be the new maximum safe speed?

$A$ body of mass $M \text{ kg}$ is at the top point of a smooth hemisphere of radius $5 \text{ m}$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \text{ m/s}$. At this instant, the angle made by the radius vector of the body with the vertical is (Acceleration due to gravity $g = 10 \text{ m/s}^2$) (in $^{\circ}$)

$A$ coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table is halved,it will just slip when placed at a distance of $............\,cm$ from the center.