A plank with a small block on top of it is under going vertical $SHM.$ Its period is $2\, sec.$ The minimum amplitude at which the block will separate from plank is :
Medium
Download our app for free and get started
Here $g=A \omega^{2}$
$\mathrm{A}=\frac{\mathrm{g}}{\omega^{2}}=\frac{\mathrm{g}}{\left(\frac{2 \pi}{\mathrm{T}}\right)^{2}}=\frac{\mathrm{gT}^{2}}{4 \pi^{2}}$
$A=\frac{10 \times 4}{4 \pi^{2}}=\frac{10}{\pi^{2}} \mathrm{m}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A $S.H.M.$ is represented by $x = 5\sqrt 2 (\sin 2\pi t + \cos 2\pi t).$ The amplitude of the $S.H.M.$ is .... $cm$View Solution
- 2$x$ and $y$ displacements of a particle are given as $x(t) = a\,sin\,\omega t$ and $y(t) = a\,sin\,2\omega t.$ Its trajectory will look likeView Solution
- 3Two masses $m_1$ and $m_2$ are supended together by a massless spring of constant $k$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system; the amplitude of vibration isView Solution
- 4The general displacement of a simple harmonic oscillator is $x = A \sin \omega t$. Let $T$ be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t=\frac{T}{\beta}$. The value of $\beta$ is $.........$View Solution
- 5In the figure shown, there is friction between the blocks $P$ and $Q$ but the contact between the block $Q$ and lower surface is frictionless. Initially the block $Q$ with block $P$ over it lies at $x=0$, with spring at its natural length. The block $Q$ is pulled to right and then released. As the spring - blocks system undergoes $S.H.M.$ with amplitude $A$, the block $P$ tends to slip over $Q . P$ is more likely to slip atView Solution
- 6A spring is stretched by $5 \,\mathrm{~cm}$ by a force $10 \,\mathrm{~N}$. The time period of the oscillations when a mass of $2 \,\mathrm{~kg}$ is suspended by it is :(in $s$)View Solution
- 7One-forth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will beView Solution
- 8A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4 m$ is suspended from the same springView Solution
- 9A block of mass $m$ is suspended separately by two different springs have time period $t_1$ and $t_2$ . If same mass is connected to parallel combination of both springs, then its time period will beView Solution
- 10A $15 \,g$ ball is shot from a spring gun whose spring has a force constant of $600 \,N/m$. The spring is compressed by $5 \,cm$. The greatest possible horizontal range of the ball for this compression is .... $m$ ($g = 10 \,m/s^2$)View Solution