The minimum force required to start pushing a body up a rough (having co-efficient of friction $\mu$ ) inclined plane is $\vec{F}_1$ while the minimum force needed to prevent it from sliding is $\overrightarrow{F_2}$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta=2 \mu$, then the ratio $F_1 / F_2$ is

A force $\vec{F}=a \hat{i}+b \hat{j}+c \hat{k}$ is acting on a body of mass $m$. The body was initially at rest at the origin. The co-ordinates of the body after time ' $t$ ' will be

What force $$\mathrm{F}$$ is required to start moving this $$10 \mathrm{~kg}$$ block shown in the figure if it acts at an angle of $$60^{\circ}$$ as shown? $$(\mu_s=0.6)$$

A body of mass 2 kg moves in a horizontal circular path of radius 5 m. At an instant, its speed is 2$$\sqrt5$$ m/s and is increasing at the rate of 3 m/s$$^2$$. The magnitude of force acting on the body at that instant is,