Question

A steel ball is dropped from a height h and it makes a perfectly elastic collision with a horizontal plane. Following its initial release, it will make a periodic motion with frequency____?

• A. $2\pi \sqrt{\frac{g}{h}}$
• B. $2\pi \sqrt{\frac{8}{h}}$
• C. $\frac{1}{2}\sqrt{\frac{g}{2h}}$
• D. $\frac{1}{2}\sqrt{\frac{2h}{g}}$

Answer 1

The correct option is C $\frac{1}{2}\sqrt{\frac{g}{2h}}$

$h=\frac{1}{2}gt$
$t=\sqrt{\frac{2h}{g}}$
$t_{total}=2t-2\sqrt{\frac{2h}{g}}$
$f=\frac{1}{t_{total}}=\frac{1}{2}\sqrt{\frac{g}{2h}}$