At any time ' $t$ ', the co-ordinates of moving particle are $x=a t^2$ and $y=b t^2$. The speed of the particle is

A radioactive element A decays into radioactive element C by the following processes in succession.

$\mathrm{A} \rightarrow \mathrm{B}+{ }_2 \mathrm{H}_{\mathrm{e}}^4 ; \mathrm{B} \rightarrow \mathrm{C}+2 \mathrm{e}^{-}$Then elements

A thin metal wire of length ' L ' and mass ' M ' is bent to form semicircular ring as shown. The moment of inertia about $\mathrm{XX}^{\prime}$ is

A particle executes S.H.M. starting from the mean position. Its amplitude is ' a ' and its periodic time is ' $T$ '. At a certain instant, its speed ' $u$ ' is half that of maximum speed $\mathrm{V}_{\text {max }}$. The displacement of the particle at that instant is