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AP EAMCET · PHYSICS · Mechanical Properties of Solids

A sphere of mass \(2 \mathrm{~kg}\) and diameter \(4.5 \mathrm{~cm}\) is attached to the lower end of a steel wire of \(2 \mathrm{~m}\) length and area of cross-section \(0.24 \times 10^{-6} \mathrm{~m}^2\). The wire is suspended from \(205 \mathrm{~cm}\) high ceiling of a room. When the system is made to oscillate as a simple pendulum, the sphere just grazes the floor at its lowest position. The velocity of the sphere at the lowest position is (Young's modulus of steel \(=2 \times 10^{11} \mathrm{Nm}^{-2}\) and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

  1. A \(10 \mathrm{~ms}^{-1}\)
  2. B \(12 \mathrm{~ms}^{-1}\)
  3. C \(15 \mathrm{~ms}^{-1}\)
  4. D \(18 \mathrm{~ms}^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(10 \mathrm{~ms}^{-1}\)

Step-by-step Solution

Detailed explanation

Extension in wire due to load and centrifugal force \( =\Delta l=(205-204.5) \mathrm{cm}=0.5 \mathrm{~cm} \) If velocity of sphere at lowest point is \(v\), then…