1
After the collision the disk starts to rotate around point C in the XY plane. The maximum change in the height (in m) of its center O is:
Answer
0.14 to 0.16
Solution
Key idea: angular momentum about the pivot C is conserved in the collision (pivot impulse has no torque about C).
Take C as origin: P= (R 45 , -R-R 45 )=(0.1414, -0.3414) m.
Lz=xpy-ypx. Before: p=(-2,0), L=-0.3414 2=-0.6828. After: p=(0,-1.8), L=0.1414 (-1.8)=-0.2546 kg m2s-1.
Disk: IC= 32MR2=0.06 kg m2, IC =0.6828-0.2546=0.4283 =7.14 rad s-1.
K= 12IC 2= (0.4283)22 0.06=1.529 J=Mgh h= 1.52910=0.153 m (less than 2R, so the disk swings back).
Answer: 0.15 (accepted range 0.14 to 0.16)
JEE Advanced 2026 Paper 2