The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )
JEE MAIN 2022, Medium
Download our app for free and get started
$T =2 \pi \sqrt{\frac{ L }{ g }}, \quad g ^{\prime}=\frac{ GM }{9 R ^{2}}=\frac{ g }{9}=\frac{\pi^{2}}{9}$
$2=2 \pi \sqrt{\frac{ L }{\pi^{2}} \times 9}$
$1=\pi \sqrt{ L } \times \frac{3}{\pi} \Rightarrow L =\frac{1}{9}\,m$
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
- 1View SolutionWhen the displacement is half the amplitude, the ratio of potential energy to the total energy is
- 2A body of mass $5\, gm$ is executing $S.H.M.$ about a point with amplitude $10 \,cm$. Its maximum velocity is $100\, cm/sec$. Its velocity will be $50\, cm/sec$ at a distanceView Solution
- 3A particle of mass m is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = - kx + {F_0}$ in which $k$ and ${F_0}$ are constants. The particle when disturbed will oscillateView Solution
- 4View SolutionIn case of a simple pendulum, time period versus length is depicted by
- 5A rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by spring on block is $.......N$.View Solution
- 6View SolutionIn a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
- 7$Assertion :$ The amplitude of an oscillating pendulum decreases gradually with timeView Solution
$Reason :$ The frequency of the pendulum decreases with time. - 8A simple perdulum performs simple harmonic motion about $x=0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x=a/2$ will beView Solution
- 9The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ isView Solution
- 10The displacements of two particles executing $S.H.M.$ on the same line are given. as $y_1=a \sin \left(\frac{\pi}{2} t+\phi\right)$ and $y_2=b \sin \left(\frac{2 \pi}{3} t+\phi\right)$. The phase difference between them at $t=1 \,s$ is .........View Solution