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

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

Tardigrade Admin · Accepted Answer

Here, a = 1 cm = 0.01 mÍ¾ The mass will remain in contact with surface, if mg=mω2a or ω=√g/a or 2π upsilon=√g/a or upsilon=(1/2π)√(g/a) upsilon=(7/2×22)√(980/1)=4.9 s-1=5 Hz

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

5 Hz

0.5 Hz

1.5 Hz

10 Hz

Here, $a = 1 c m = 0.01 m$ ; The mass will remain in contact with surface, if
$m g = m ω^{2} a$ or $ω = g / a$
or $2 π υ = g / a$ or $υ = \frac{1}{2 π} \frac{g}{a}$
$υ = \frac{7}{2 \times 22} \frac{980}{1} = 4.9 s^{- 1} = 5 Hz$

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