An ideal string is wrapped several times on a solid cylinder of mass 4 kg and radius 1 m. The pulleys are ideal and the surface between block and ground is smooth. Cylinder rolls without slipping on the block. If the torque acting on the cylinder is 10x/9 N-m, then find the value of x.
Physics · Mixed Chapter
JEE Mains

Question

An ideal string is wrapped several times on a solid cylinder of mass 4 kg and radius 1 m. The pulleys are ideal and the surface between block and ground is smooth. Cylinder rolls without slipping on the block. If the torque acting on the cylinder is 10x/9 N-m, then find the value of x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let the accelerations of the 8 kg block, cylinder centre and cylinder spin be aᵦ, a꜀ and α. Write the string-length constraint for the fixed and moving pulleys, together with the pure-rolling constraint a꜀−Rα=aᵦ. Step 2: Apply Newton's second law to the block and cylinder and rotational equation Iα=τ for the solid cylinder, I=½(4)(1)²=2 kg m². Step 3: Solving these coupled constraints gives the magnitude of torque τ=80/9 N m. Step 4: Compare 80/9=10x/9; hence x=8.