A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The speed of a transverse wave in the rope at a point 0.5 m distant from the lower end is √(2.45 × n), where n = _____.
Physics · Mixed Chapter
JEE Mains

Question

A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The speed of a transverse wave in the rope at a point 0.5 m distant from the lower end is √(2.45 × n), where n = _____.

G1 Physics · Accepted Answer

Step 1: At height y above the free end of a vertically suspended uniform rope, tension equals the weight below that point: F=μgy. Step 2: Wave speed v=√(F/μ)=√(gy). Step 3: With y=0.5 m and g=9.8 m s⁻², v²=4.9=2.45×2. Step 4: Therefore n=2.