Concrete mixture is made by mixing cement,stone,and sand in a rotating cylindrical drum. If the drum rotates too fast,the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to (Take the radius of the drum to be $1.25\, m$ and its axle to be horizontal).

$A$ light rigid wire of length $1 \,m$ is attached to a ball of mass $500 \,g$ at one end. The other end of the wire is fixed, so that the wire can rotate freely in the vertical plane about its fixed end. At the lowest point of the circular motion, the ball is given a horizontal velocity of $6 \,m/s$. Determine the radial component of the acceleration of the ball when this rigid wire makes an angle of $60^{\circ}$ with the upward vertical. (Take $g = 10 \,m/s^2$) (in $\,m/s^2$)

$A$ body of mass '$m$' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ($g =$ gravitational acceleration)

$A$ weightless string can support a tension up to $30 \,N$. $A$ stone of mass $0.5 \,kg$ is tied to its one end and is revolved in a circular path of radius $2 \,m$ in a vertical plane. Then the maximum angular velocity of the stone will be (acceleration due to gravity $g=10 \,m/s^2$)

In order to just complete the vertical circular motion,the ratio of kinetic energy of a particle at the highest point to that at the lowest point is

$A$ stone of mass $m$ tied to the end of a string revolves in a vertical circle of radius $R$. The net forces at the lowest and highest points of the circle directed vertically downwards are:

Lowest Point	Highest Point
$(a) \ mg - T_1$	$mg + T_2$
$(b) \ mg + T_1$	$mg - T_2$
$(c) \ mg + T_1 - \frac{mv_1^2}{R}$	$mg - T_2 + \frac{mv_2^2}{R}$
$(d) \ mg - T_1 - \frac{mv_1^2}{R}$	$mg + T_2 + \frac{mv_2^2}{R}$

$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.