A cylinder of height h is placed on an inclined plane it just begins to slide on increasing angle of 45degrees what is the radius of the cylinder

Asked by sandhyamsani 20th March 2017, 7:33 PM

Answered by Expert

Answer:

The force of friction 'f' is the force that is responsible for producing the translatory equilibrium (the state of equilibrium in which the motion changes dynamically).
But it also produces a torque which tries to overturn the block= $begin mathsize 12px style straight f straight h over 2 end style$
The restoring torque due to normal reaction 'N' opposes this through a distance 'x'.
Therefore, for 'no overturning of the cylinder' is $straight f straight h over 2 equals Nx$
As the angle of inclination of surface increases, the friction also increases but the normal reaction (N) decreases.
Due to the decrease in normal reaction, the chances of overturning increases.

To counterbalance the overturning, N has to shift up to an extreme level of x=r, where r is the radius of the given cylinder.
Therefore for 'just' no overturning. $begin mathsize 12px style straight f straight h over 2 equals straight N cross times straight r end style$
This condition is only possible at angle=45 degree.
As, $begin mathsize 12px style straight theta equals 45 to the power of straight o comma space cos space straight theta equals Sin space straight theta end style$ f (f= mg Sin $begin mathsize 12px style straight theta end style$ )=N (mg Sin $begin mathsize 12px style straight theta end style$ ), thus $begin mathsize 12px style straight h equals straight r over 2 end style$ .