The velocity of a particle executing SHM varies with displacement $( x )$ as $4 v ^2=50- x ^2$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is $............$ $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$
JEE MAIN 2023, Medium
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
- 1The amplitude of a damped oscillator becomes half in one minute. The amplitude after $3$ minute will be $\frac{1}{X}$ times the original, where $X$ isView Solution
- 2A 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 .... $Hz$View Solution
- 3A particle executes $SHM$ of amplitude $25\, cm$ and time period $3\, s$. What is the minimum time required for the particle to move between two points $12.5\, cm$ on either side of the mean position ..... $\sec$View Solution
- 4Four harmonic waves of equal frequencies and equal intensities $I_0$ have phase angles $0, \pi / 3,2 \pi / 3$ and $\pi$. When they are superposed, the intensity of the resulting wave is $nI _0$. The value of $n$ isView Solution
- 5If a spring extends by $x$ on loading, then energy stored by the spring is (if $T$ is the tension in the spring and $K$ is the spring constant)View Solution
- 6A ring of diameter $2m$ oscillates as a compound pendulum about a horizontal axis passing through a point at its rim. It oscillates such that its centre move in a plane which is perpendicular to the plane of the ring. The equivalent length of the simple pendulum is .... $m$View Solution
- 7View SolutionThe total spring constant of the system as shown in the figure will be
- 8An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross$-$section, $A$. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction isView Solution
- 9View SolutionThe velocity of a particle performing simple harmonic motion, when it passes through its mean position is
- 10Find 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)View Solution
