test tube cracked when added glycerin to potassium permanganate
I am not sure I should continue on sulfuric acid and potassium parmagnet test in a TEST TUBE after seeing this affect...


In case of doubt you should not. Anyway, I recommend to avoid doing it with any significant amount. It may and will spread around and even if not it produces manganese (IV) oxide smoke that settles down nearby and is quite hard to wash out. 


  I want to know why, because it lab we some time directly heat test tube, it does not cracked so why this time..


Potassium permanganate is a strong oxidizer, glycerol is a reducer. Mixed together they quickly start to react. The exact nature of the products is debatable, but the mixture self-ignites if warm. The thermal shock is enough to crack glass. This is a common weakness of glass and ceramics. 

Furthermore, in case of bad luck it may produce enough gases to spread the mix around. Consequently, safety precautions must be always employed (incombustible table, safety goggles etc). A movie how it may go http://www.youtube.com/watch?v=6F4cuQkKt2U . The reaction has some quirks, specifically if the glycerol is cold, it may not start immediately, so a rather well mixing is achievable. Now, once it warms up to room temperature, it suddenly bursts in flame, potentially delivering itself to nearby surfaces, including your face.