Question

One end of a long metallic wire of length \( L \) tied to the ceiling. The other end is tied with a massless spring of spring constant \( K \). A mass hangs freely from the free end of the spring. The area of cross section and the Young’s modulus of the wire are \( A \) and \( Y \) respectively. If the mass slightly pulled down and released, it will oscillate with a time period \( T \) equal to:

• A. \( 2\pi \sqrt{\frac{m}{K}} \)
• B. \( 2\pi \sqrt{\frac{m(YA + KL)}{YAK}} \)
• C. \( 2\pi \sqrt{\frac{mYA}{KL}} \)
• D. \( 2\pi \sqrt{\frac{m}{L}} \)

Hint:

The time period of a system involving a spring and a wire depends on the spring constant, the mass, and the Young's modulus.

Answer 1

The Correct Option is B