A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear density of 19.2 × 10⁻³ kg/m. The speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2.0 m/s² is 12.5n. What is the value of n? Take g = 10 m/s² and m_string ≪ 4 kg.
Physics · Mixed Chapter
JEE Mains

Question

A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear density of 19.2 × 10⁻³ kg/m. The speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2.0 m/s² is 12.5n. What is the value of n? Take g = 10 m/s² and m_string ≪ 4 kg.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Upward elevator acceleration raises the apparent weight of the block, so string tension is F=m(g+a)=4(10+2)=48 N. Step 2: The linear density is μ=19.2×10⁻³=0.0192 kg m⁻¹. Step 3: Wave speed v=√(F/μ)=√(48/0.0192)=√2500=50 m/s. Step 4: From v=12.5n, n=50/12.5=4.