The co-ordinates of the centre of mass of a uniform $L$ shaped plate of mass 3 kg shown in the figure is

A circular disc of mass 20 kg and radius 1 m is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity of $2 \mathrm{rad} \mathrm{s}^{-1}$. Then, the rotational kinetic energy of the disc is

The equations for the displacements of two particles in simple harmonic motion are $y_1=0.1 \sin \left(100 \pi t+\frac{\pi}{3}\right)$ and $y_2=0.1 \cos \pi t$ respectively. The phase difference between the velocities of the two particles at a time $t=0$ is

A spring is stretched by 0.2 m when a mass of 0.5 kg is suspended to it. The time period of the spring when 0.5 kg mass is replaced with a mass of 0.25 kg is suspended to it is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )