A block $m$ slides down a curved frictionless track, starting from rest. The curve obeys the equation $y=\frac{x^2}{2}$. The tangential acceleration of the block is

Two particles start moving on circles of radius $R_1=1 \mathrm{m}$ and $R_2=3 \mathrm{m}$ shown with velocity $v_1=2 \mathrm{m} {\mathrm{s}}^{-1}, v_2=15 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The minimum time after which the particles will again be collinear with centre is equal to

As shown in figure, a mass $m$ is rotating freely in a horizontal circle of radius $20 \mathrm{cm}$ in a smooth fixed cone which supports a stationary mass $m$ attached to the other end of the string passing through smooth hole $O$ in cone hanging vertically. Find the angular velocity of rotation $\left(\sin 53°=\frac{4}{5}\right)$.