A $500 \,kg$ car takes a round turn of radius $50 \,m$ with a velocity of $36 \,km/hr$. The centripetal force is ..........  $N$

A small mass $'m'$ rests at the edge of a horizontal disc of radius $'R'$ . The coefficient of static friction between mass and the disc is $\mu $ . The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $'h'$ meters below. What was its horizontal distance of travel from the point it left the disc?

Concretemixture 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 motorcycle is going on an overbridge of radius $R$. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal forces on it is

A string breaks if its tension exceeds $10$ newtons. A stone of mass $250\, gm$ tied to this string of length $10 \,cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be ..........  $rad/s$

A train is moving with a speed of $12 \mathrm{~m} / \mathrm{s}$ on rails which are $1.5 \mathrm{~m}$ apart. To negotiate a curve radius $400 \mathrm{~m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=$ $10 \mathrm{~m} / \mathrm{s}^2$ ) :