Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction,the magnitude of the minimum additional force needed is ........... $N$.

$A$ rough inclined plane $BCE$ of height $\left(\frac{25}{6}\right) \text{ m}$ is kept on a rectangular wooden block $ABCD$ of height $10 \text{ m}$,as shown in the figure. $A$ small block is allowed to slide down from the top $E$ of the inclined plane. The coefficient of kinetic friction between the block and the inclined plane is $\frac{1}{8}$ and the angle of inclination of the inclined plane is $\sin^{-1}(0.6)$. If the small block finally reaches the ground at a point $F$,then $DF$ will be (Acceleration due to gravity,$g=10 \text{ ms}^{-2}$)

$A$ force $F = Kt$ (where $t$ is the time in seconds and $K = 2 \, N/s$) is applied on a $2 \, kg$ block at $t = 0$ as shown in the figure. The displacement of the $8 \, kg$ block until the time when the $2 \, kg$ block starts slipping on the $8 \, kg$ block will be (coefficient of friction between the $2 \, kg$ block and the $8 \, kg$ block is $0.2$ and between the $8 \, kg$ block and the surface is zero,$g = 10 \, m/s^2$).

$A$ ball connected with a string is released at an angle of $45^{\circ}$ with the vertical,as shown in the figure. If the mass of the box is equal to the mass of the ball,the acceleration of the box at this instant will be:

$A$ truck of mass $M$ is at rest on a frictionless road when a monkey of mass $m$ starts moving on the truck in the forward direction. If the truck recoils with a speed $v$ backward on the road,with what velocity is the monkey moving with respect to the truck?

$A$ body is imparted motion from rest to move in a straight line. If it is then obstructed by an opposite force,then: