In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $$\left( {{{{I_1}} \over {{I_2}}}} \right)$$ will be x : 1. The value of x will be _____________.

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____________ $$\pi$$ $$\times$$ 10^$$-$$1 Nm.

A particle of mass 'm' is moving in time 't' on a trajectory given by

$$\overrightarrow r = 10\alpha {t^2}\widehat i + 5\beta (t - 5)\widehat j$$

Where $$\alpha$$ and $$\beta$$ are dimensional constants.

The angular momentum of the particle becomes the same as it was for t = 0 at time t = ____________ seconds.

The centre of a wheel rolling on a plane surface moves with a speed v₀. A particle on the rim of the wheel at the same level as the centre will be moving at a speed $$\sqrt x {v_0}$$. Then the value of x is _____________.