A book is resting on a shelf that is undergoing vertical simple h… - Vidyadip

MCQ

A book is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of $2.5 \,cm$. What is the minimum frequency of oscillation of the shelf for .......... $Hz$ the book will lose contact with the shelf? (Assume that, $g=10 \,ms ^{-2}$ )

A
$20$
✓
$3.18$
C
$125.6$
D
$10$

✓

Answer

Correct option: B.

$3.18$

b
(b)

Book started to loose contact with shelf when maximum acceleration $a$ of shelf is such that,

$a_{\max } \geq g$

$\Rightarrow \quad \omega^2 A \geq g$

$\Rightarrow \quad \omega^2=\frac{g}{A}$.

So, frequency of oscillations is

$f=\frac{\omega}{2 \pi}=\frac{1}{2 \pi} \sqrt{\frac{g}{A}}$

$\Rightarrow \quad f=\frac{1}{2 \pi} \cdot \sqrt{2.5 \times 10^{-2}}=\frac{2 \times 10}{2 \pi}$

$\Rightarrow \quad f \approx 3.18 \,Hz$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Figure shows three similar lamp. $L_1,L_2$ and $L_3$ connected across a power supply. If the lamp $L_3$ fuses, how will the light emitted by $L_1$ and $L_2$ change ?

A solid cylinder of mass $3 \ kg$ is rolling on a horizontal surface with velocity $4\ m s^{- 1}$. It collides with a horizontal spring of force constant $200\ Nm^{-1}$. The maximum compression produced in the spring will be $............... \mathrm{m}$

A particle of mass $m$ is projected at an angle $\alpha $ to the horizontal with initial velocity $u\,m/s$ then work done by gravity during the time it reaches its highest point

What is the shortest wavelength present in the Paschen series of spectral lines?

In Young’s expt., the distance between two slits is $\frac {d}{3}$ and the distance between the screen and the slits is $3\,D$. The number of fringes in $\frac {1}{3}\,m$ on the screen, formed by monochromatic light of wavelength $3\,\lambda $, will be

A pipe of length $1.5\ m$ closed at one end is filled with gas and resonates in its fundamental mode with a tuning fork. Another open organ pipe of same dimensions filled with air resonates in its fundamental mode with same tuning fork. If experiment is performed at $30\,^oC$ (speed of sound in air is $360\ m/sec$ at $30\,^oC$), the speed of sound at $0\,^oC$ in gas is ...... $m/sec$ (Neglect end correction)

The equivalent capacitance of the system shown in the following circuit is $...........\mu F$

A coin, placed on a rotating turn-table slips, when it is placed at a distance of $9 \,cm$ from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is ......... $cm$.

A signal $A\,cos\,\omega \,t$ is transmitted using ${v_0}\,\sin \,{\omega _0}t$ as carrier wave. The correct amplitude modulated $(AM)$ signal is

An object is placed at a distance of $40\,\, cm$ from a concave mirror of focal length $15\,\, cm.$ If the object is displaced through a distance of $20\,\, cm$ towards the mirror, the displacement of the image will be