A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by $n^{2}R{t}^2$, where $n$ is a constant. The power delivered to the particle by the force acting on it, is :

The boxes of masses $2 \mathrm{kg}$ and $8 \mathrm{kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8 \mathrm{kg}$ to strike the ground starting from rest.  $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ 

The resultant of these forces $\overrightarrow{OP},\overrightarrow{OQ},\overrightarrow{OR},\overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately ______$\mathrm{N}.$
[Take $\sqrt{3}=1.7,\sqrt{2}=1.4$ Given $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ unit vectors along $x, y$ axis]

The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _______$\mathrm{N}$ (take $\left.g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$