$A$ disc of mass $0.2 \ kg$ is kept floating in air without falling by vertically firing bullets each of mass $0.05 \ kg$ on the disc at the rate of $10$ bullets per second. If the bullets rebound with the same speed,then the speed of each bullet is (Acceleration due to gravity $g = 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

An infinite number of masses are placed on a frictionless table and they are connected via massless strings. Their masses follow the sequence $m, \frac{m}{2}, \frac{m}{6}, \ldots, \frac{m}{n!}, \ldots$ and they are further connected to a mass $m$ that hangs over a massless pulley. The acceleration of the hanging mass is

$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively:

$A$ vehicle is moving with uniform speed along $3$ different shaped roads: horizontal,concave,and convex. The surface of the road on which the normal reaction on the vehicle is maximum is

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1$: If you push on a cart being pulled by a horse so that it does not move,the cart pushes you back with an equal and opposite force.
Statement $2$: The cart does not move because the forces described in Statement $1$ cancel each other.

What is the relationship between $W_1$ and $W_2$?