What is the minimum value of $\mathrm{F}$ needed so that block begins to move upward on frictionless incline plane as shown

The tension $\mathrm{T}$ in the string shown in figure is

An object of mass $2 \mathrm{kg}$ at rest at origin starts moving under the action of a force

$\overrightarrow{\mathrm{F}}=\left(3{\mathrm{t}}^2\hat{\mathrm{i}}+4\hat{\mathrm{t}}\hat{\mathrm{j}}\right)\mathrm{N}$

The velocity of the object at $\mathrm{t}=2 \mathrm{s}$ will be

The magnitude of force acting on a particle moving along $\mathrm{x}$-axis varies with time $\left(\mathrm{t}\right)$ as shown in figure. If at $\mathrm{t}=0$ the velocity of particle is ${\mathrm{v}}_0,$ then its velocity at $\mathrm{t}={\mathrm{T}}_0$ will be

Tension in the rope at the rigid support is $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$