A body of mass $10 \mathrm{kg}$ lies on a rough inclined plane of inclination $\theta ={\sin }^{-1}\frac{3}{5}$ with the horizontal. When a force of $30 \mathrm{N}$ is applied on the block parallel to and upward the plane, the total reaction by the plane on the block is nearly along:

The system is pushed by a force $F$ as shown in figure. All surfaces are smooth except between $B$ and $C$. The friction coefficient between $B$ and $C$ is $\mu$. The minimum value of $F$ to prevent block $B$ from downward slipping is,

A force $F=t$ is applied to a block $A$ as shown in figure where $t$ is time in seconds. The force is applied at $t=0 \mathrm{s}$ when the system was at rest. Which of the following graph correctly gives the frictional force between $A$ and horizontal surface as a function of time $t$. Assume that at $t=0$, the tension in the string connecting the two blocks is zero.

A force $F=2t$ (where $t$ is the time, in seconds). The force is applied at $t=0 \mathrm{s}$ to the block of mass $m$ placed on a rough horizontal surface. The coefficient of static and kinetic friction between the block and surface are ${\mu }_{\mathrm{s}}$ and ${\mu }_{\mathrm{k}}$, respectively. Which of the following graphs best represents the acceleration vs time of the block .