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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

  • 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 Sinbegin mathsize 12px style straight theta end style)=N (mg Sinbegin mathsize 12px style straight theta end style), thus begin mathsize 12px style straight h equals straight r over 2 end style.
Answered by Expert 21st March 2017, 5:56 PM
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