Question

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to a massless spring of spring constant $K.A$ mass $m$ hangs freely from the free end of the spring. The area of cross-section and the young's modules of the wire $A$ and $Y$, respectively. If the mass is 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. $2\pi \sqrt{\frac{mL}{YA}}$

Answer 1

The correct option is A $2\pi \sqrt{\frac{m}{K}}$

Time period of oscillation will only depend upon, Tension in spring at attached point block . Metallic wire won't effect Time period of block

$T=Kx$

so Time period is of such system is given by

$T=2\pi \sqrt{\frac{m}{k}}$

where $k=K$ in this case.

$T=2\pi \sqrt{\frac{m}{K}}$