Question

A large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1\, cm$. If a mass of $10\, kg$ (which is placed on the surface) is to remain continuously in contact with it, the maximum frequency of S.H.M. will be

• A. 5 Hz
• B. 0.5 Hz
• C. 1.5 Hz
• D. 10 Hz

Answer 1

Answer: (A)

5 Hz

Answer 2

Here, $a\, = \,1 \,cm = 0.01\, m$; The mass will remain in contact with surface, if $mg=m\omega^{2}a$ or $\omega=\sqrt{g/a}$ or $2\pi\upsilon=\sqrt{g/a}$ or $\upsilon=\frac{1}{2\pi}\sqrt{\frac{g}{a}}$ $\upsilon=\frac{7}{2\times22}\sqrt{\frac{980}{1}}=4.9\,s^{-1}=5\,Hz$