Question

If two wires of same length l and area of cross section A with Young modulus Y and 2Y connect in series and one end is fixed on roof and other end with mass m. Make simple harmonic motion, then the time period is -

• A. $2\pi\sqrt{\frac{m\mathcal{l}}{YA}}$
• B. $2\pi\sqrt{\frac{m\mathcal{l}}{3YA}}$
• C. $2\pi\sqrt{\frac{3m\mathcal{l}}{2YA}}$
• D. $2\pi\sqrt{\frac{m\mathcal{l}}{2YA}}$

Answer 1

Answer: (C)

$2\pi\sqrt{\frac{3m\mathcal{l}}{2YA}}$

Answer 2

The force constant of wires are

k₁ = $\frac{YA}{\mathcal{l}}$, k₂ = $\frac{2YA}{\mathcal{l}}$

In series k = $\frac{k_{1}k_{2}}{k_{1} + k_{2}}$ = $\frac{2}{3}\left( \frac{YA}{\mathcal{l}} \right)$

T = $2\pi\sqrt{\frac{3m\mathcal{l}}{2YA}}$