A ball with mass $m$ projected horizontally off the end of a table with an initial kinetic energy $K$. At a time $t$ after it leaves the end of the table it has kinetic energy $3K$. What is $t$? Neglect air resistance.

In the figure shown the potential energy $\left(U\right)$ of a particle is plotted against its position '$x$' from origin. Then which of the following statement is correct. A particle at:

The teeter toy consists of two identical weights which hang form a peg on drooping arms as shown in the figure. The arrangement is unexpectedly stable. The toy can be spun or rocked with little danger of toppling over. For simplicity consider only rocking motion in the vertical plane. For the teeter toy to be stable

The given plot shown the variation, the potential energy $\left(U\right)$ of interaction between two particle with the separating distance $\left(r\right)$ between them. Which of the above statements are correct?

(1) $B$ and $D$ are equilibrium points 

(2) $C$ is a point of stable equilibrium points 

(3) The force of interaction between the two particle is attractive between points $C$ and $D$ and repulsive between points between $D$ and $E$ on the curve.

(4) The force of interaction between the particles is repulsive between points $E$ and $F$ on the curve.

A weight is hung freely from the end of a spring. A boy then slowly pushes the weight upwards until the spring become slack. The gain in gravitational energy of the weight during this process is equal to:

A block attached to spring, pulled by a constant horizontal force $F$, is kept on a smooth surface as shown in the figure. Initially, the spring is in its natural state. Then the maximum positive work that the applied force $F$ can do is :[ Given that spring does not break]