A uniform cylinder of radius R(=3 ~m ) is spin about its axis at an angular velocity ₀(=40 rad / sec ) and placed between two perpendicular wall. The coefficient of friction between the walls and cylinder is (=2) . Then, 25 K turns will the cylinder make before it stops. Find the value of K.

Step-by-step solution

aligned & N ₁+ N ₂= mg ...(i) & N ₁= N ₂....(ii) & ~N ₂= mg (1+ ^2 ) & N ₁= mg (1+ ^2 ) aligned Torque about centre of mass aligned & (N₁+N₂ ) R= 1 2 m R^2 & = 2 (N₁+N₂ ) m R = 2 (1+ ) g (1+ ^2 ) R & ^2= ₀^2-2 & = ₀^2 2 & = ₀^2 (1+ ^2 ) R 2 2 (1+ ) g aligned Hence number of turns aligned & N= 2 = ₀^2 R (1+ ^2 ) 4 (1+ ) g 2 & N= ₀^2 R (1+ ^2 ) 8 g(1+ ) aligned