A solid sphere of radius \(4a\) units is placed with its centre at origin. Two charges \(-2q\) at \((-5a, 0)\) and \(5q\) at \((3a, 0)\) is placed. If the flux through the sphere is \(\frac{xq}{\in_0}\) , find \(x\)
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure. 
The angular velocity of the system after the particle sticks to it will be: