Find maximum amplitude for safe $SHM$ (block does not topple during $SHM$) of $a$ cubical block of side $'a'$ on a smooth horizontal floor as shown in figure (spring is massless)
A$\frac{{mg}}{{3K}}$
B$\frac{{3mg}}{K}$
C$\frac{{2mg}}{{3K}}$
D
None
Diffcult
Download our app for free and get started
B$\frac{{3mg}}{K}$
b $\tau=0, \quad K x\left(\frac{a}{6}\right)=\frac{N a}{2} \Rightarrow K x \frac{a}{6}=m g \frac{a}{2} \Rightarrow x=\frac{3 m g}{K}$
Download our app
and 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.*
A block is placed on a frictionless horizontal table. The mass of the block is m and springs are attached on either side with force constants ${K_1}$ and ${K_2}$. If the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be
The maximum speed of a particle executing $S.H.M.$ is $1\,m/s$ and its maximum acceleration is $1.57\,m/se{c^2}$. The time period of the particle will be .... $\sec$
$A$ block of mass $M_1$ is hanged by a light spring of force constant $k$ to the top bar of a reverse Uframe of mass $M_2$ on the floor. The block is pooled down from its equilibrium position by $a$ distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$ -frame will leave the floor momentarily.
The time period of oscillations of a simple pendulum is $1$ minute. If its length is increased by $44 \%$. then its new time period of oscillation will be ......... $s$
The displacement time equation of a particle executing $SHM$ is : $x = A \,sin\,(\omega t + \phi )$. At time $t = 0$ position of the particle is $x = A/2$ and it is moving along negative $x-$ direction. Then the angle $\phi $ can be
A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be
The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\ s$. In another $10\ s$ it will decrease to $\alpha $ times its original magnitude, where $\alpha $ equals
Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of oscillation of the two $SHM$ is $\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },$ where value of $x$ is