Question

A metre stick swinging from one end oscillates in simple harmonic motion with frequency f₀. If the bottom half of the stick were cut off, then its new oscillation frequency would be:

• A. f₀
• B. √2f₀
• C. 2f₀
• D. 2 √2 f₀

Answer 1

Answer: (B)

√2f₀

Answer 2

f₀ = $\frac{1}{2\pi}\sqrt{\frac{mgl}{I}}$

where l is distance between point of suspension and centre of

mass of the body.Thus for the stick of length L and mass m.

f₀ = $\frac{1}{2\pi}\sqrt{\frac{mg.\frac{L}{2}}{\left( mL^{2}/12 \right)}} = \frac{1}{2\pi}\sqrt{\frac{6g}{L}}$

when bottom half of the stick is cut off

f₀' = $\frac{1}{2\pi}\sqrt{\frac{\frac{m}{2}g.\frac{L}{4}}{\frac{m}{2}.\frac{(L/2)^{2}}{12}}} = \frac{1}{2\pi}\sqrt{\frac{12g}{L}} = \sqrt{2}$