In Searle’s experiment wire diameter d=0.050 cm (least count 0.01 cm), length L=110.0 cm (least count 0.1 cm), and extension ΔL=0.125 cm (least count 0.01 cm). The weight is exactly 50 N. Maximum fractional error in Young’s modulus is approximately x/10. Find x.
Physics · Mixed Chapter
JEE Mains

Question

In Searle’s experiment wire diameter d=0.050 cm (least count 0.01 cm), length L=110.0 cm (least count 0.1 cm), and extension ΔL=0.125 cm (least count 0.01 cm). The weight is exactly 50 N. Maximum fractional error in Young’s modulus is approximately x/10. Find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Expression for Young’s modulus: Y = 4FL/(πd²ΔL). Step 2 — Maximum relative error with force exact: δY/Y = δL/L +2δd/d+δ(ΔL)/ΔL. Step 3 — Use the supplied instrument least counts as limiting errors: δY/Y = 0.1/110.0 +2(0.01/0.050)+(0.01/0.125). Step 4 — Evaluate: δY/Y≈0.00091+0.400+0.080=0.4809≈0.5. Step 5 — Match x/10: x/10≈0.5 ⇒ x=5. Answer: 5.