Let’s evaluate each option:
1. Option (A): - The green manganate ion \((\text{MnO}_4^{2-})\) is paramagnetic, not diamagnetic. The permanganate ion \((\text{MnO}_4^{-})\) is also paramagnetic, not diamagnetic. Hence, this statement is incorrect.
2. Option (B): - Interstitial compounds of transition metals do tend to have higher melting points than pure transition metals due to the presence of extra atoms that enhance the metallic bonding. Their compounds are usually less reactive. Thus, this statement is incorrect.
3. Option (C): - Cerium (Ce) is a lanthanoid metal that exhibits a stable oxidation state of \(+4\) as well as the oxidation state of \(+3\). Cerium is unique because it can stabilize both these oxidation states, making this statement correct.
4. Option (D): - Chromium (Cr) in the \(+6\) oxidation state is a strong oxidizing agent, while Tungsten (W) in the \(+6\) oxidation state is more stable.
Thus, this statement is incorrect. Therefore, the correct statement is (C): Cerium exists in both +4 and +3 oxidation states, with the +4 oxidation state being the most stable.
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: