Two small blocks each having a mass of 3.2 kg are connected by wire CD and the system is suspended from the ceiling by another vertical wire AB with AB wire connected (fixed) to the midpoint of wire CD. Linear mass density of wire AB is 10 g/m and that of CD is 80 g/m. If ratio of speeds of transverse pulse in AB to CD is 4/n, find n.
Physics · Mixed Chapter
JEE Mains

Question

Two small blocks each having a mass of 3.2 kg are connected by wire CD and the system is suspended from the ceiling by another vertical wire AB with AB wire connected (fixed) to the midpoint of wire CD. Linear mass density of wire AB is 10 g/m and that of CD is 80 g/m. If ratio of speeds of transverse pulse in AB to CD is 4/n, find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The upper wire AB bears the weight of both blocks: T_AB=2mg. Each half of horizontal wire CD supports a single block, so T_CD≈mg. Step 2: Wave speeds obey v=√(T/μ). With μ_AB=0.010 kg/m and μ_CD=0.080 kg/m, v_AB/v_CD=√[(2mg/0.010)/(mg/0.080)]. Step 3: Ratio=√16=4. Step 4: From v_AB/v_CD=4/n, n=1.