CSIR NET Dec 2015 Q97: Marine Geology

In the shallow-water (long-wave) approximation, a tsunami's propagation speed depends only on water depth: v = sqrt(g*h), where g is gravitational acceleration (~9.8 m/s^2) and h is water depth. For h = 6.25 km = 6250 m: v = sqrt(9.8 x 6250) = sqrt(61250) ≈ 247.5 m/s. The travel time to cover a distance of 1000 km = 1,000,000 m is t = distance/v = 1,000,000/247.5 ≈ 4040 seconds ≈ 67 minutes ≈ 1.1 hours, closest to option 1 (1 hr).

Option 1 is correct: applying v=sqrt(gh) with h=6.25 km gives a wave speed of about 247.5 m/s, and dividing the 1000 km distance by this speed gives a travel time of roughly 1.1 hours, best matching the 1 hr option among the given choices. Option 2 (2 hr) would require a wave speed roughly half of the computed value, inconsistent with the given depth. Option 3 (4 hr) and option 4 (8 hr) would require even slower propagation speeds, corresponding to much shallower water depths than the 6.25 km given, and are inconsistent with the shallow-water tsunami speed formula applied here.