Independent isomeric yield ratios of 1288b were determined radiochemically in the thermal neutron induced fission of /4~pu and 34 MeV alpha particle induced fission of 2asu, both involving the same compound nucleus (242pu). Fragment angular momenta estimated from the measured isomer ratios using the statistical model analysis showed significantly larger fragment angular momenta in the medium energy fissioning system compared to the low energy fissioning system. This has been attributed to the effect of higher excitation energy and angular momentum in the entrance channel leading to increased fragment temperature, moments of inertia and angular velocity. An attempt was made to calculate the fragment angular momentum in the medium energy fission using the Fermi gas model for the fissioning nucleus, taking into account the multichance fission, saddle shapes of the fissioning nuclei and the angular velocity components of the fissioning nuclei both along and orthogonal to the fission axis. The calculated angular momenta agree well with the experimental results.Nuclear Reactions: 24aPu(nth,f); 238U(c~,f); 1/*Sb; isomeric yield ratios; Fragment angular momenta PACS: 25.85.Ge; 25.85.Ec