The American naturalist Charles William Beebe (1877-1962) set a world record in 1934 when...

The American naturalist Charles William Beebe (1877-1962) set a world record in 1934 when he and Otis Barton (1899-1992) made a dive to a depth of 923 m below the surface of the ocean. The dive was made just 10 miles from Nonsuch Island, off the coast of Bermuda, in a device known as the bathysphere, designed and built by Barton. The bathysphere was basically a steel sphere 4.75 ft in diameter with three small ports made of fused quartz. Lowered in to the ocean on a steel cable whose radius was 1.85 cm, the bathysphere also carried bottles of oxygen, chemicals to absorb carbon dioxide, and a telephone line to the surface.

Charles William Beebe (left) and Otis Barton with the bathysphere in 1934. Beebe was fascinated by the new forms of life he and Barton encountered on their numerous dives. At one point he saw a “creature, several feet long, dart toward the window, turn sideways and—explode. At the flash, which was so strong that it illumined my face … I saw the great red shrimp and the outpouring fluid of flame.” No wonder he considered the ocean depths to be “a world as strange as that of Mars.”

The dives were not without their risks, however. It was not uncommon, for example, to have the bathysphere return to the surface partially filled with water after a window seal failed. On one deep dive, water began to steamrapidly into the sphere. Beebe quickly called to the surface and asked—not to be raised quickly—but to be lowered more rapidly, in the hope that increasing water pressure would force the leaking window into its seals to stop the leak. It worked, showing that Beebe was not only an exceptional naturalist, but also a cool-headed scientist with a good knowledge of basic physics!

Suppose the bathysphere and its occupants had a combined mass of 12,700 kg. How much did the cable stretch when the bathysphere was at a depth of 923 m? (Neglect the weight of the cable itself, but include the effects of the bathysphere’s buoyancy.)

A. 47 cm

B. 48 cm

C. 52 cm

D. 53 cm