Three forces $F_1=10\,N$,$F_2=8\,N$,and $F_3=6\,N$ are acting on a particle of mass $5\,kg$. The forces $F_2$ and $F_3$ are applied perpendicular to each other such that the particle remains at rest. If the force $F_1$ is removed,then the acceleration of the particle is $......\,m/s^2$.

$A$ ball of mass $0.1\, kg$ is whirled in a horizontal circle of radius $1\, m$ by means of a string at an initial speed of $10\, rpm$. Keeping the radius constant,the tension in the string is reduced to one-quarter of its initial value. The new speed is ....... $rpm$.

$A$ uniform rod $AB$ of weight $100 \, N$ rests on a rough peg at $C$ and a force $F$ acts at $A$ as shown in the figure. If $BC = CM$ and $\tan \alpha = 4/3$,the minimum coefficient of friction at $C$ is:

$A$ mass of $1 \text{ kg}$ is kept on an inclined plane with $30^\circ$ inclination with respect to the horizontal plane and it is at rest initially. Then, the whole assembly is moved up with a constant velocity of $4 \text{ m/s}$. The work done by the frictional force in time $2 \text{ s}$ is . . . . . . $\text{J}$. (Take $g = 10 \text{ m/s}^2$)

$A$ hosepipe directs a horizontal jet of water moving with a velocity of $20\, m/s$ onto a vertical wall. The cross-sectional area of the jet is $10^{-3}\, m^2$. If the density of water is $1000\, kg/m^3$,then the force acting on the wall is ........... $N$ [Assuming water comes to rest after striking the wall].

What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.