A light balloon filled with helium of density $\rho_{He}$ is tied to a light string of length $L.$ The string is tied to the ground forming an "inverted" simple pendulum (figure). If the balloon is displaced slightly from equilibrium as in figure and released, the period of the motion is. Take the density of air to be $\rho_{air}$. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.)
Advanced
Download our app for free and get started
$\tau=-(B-m g) L \theta$
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{C}}}=2 \pi \sqrt{\frac{(\mathrm{B}-\mathrm{mg}) \mathrm{L}}{\mathrm{m} \theta \mathrm{L}^{2}}}$
$\mathrm{T}=2 \pi \sqrt{\frac{\rho_{\mathrm{air}} \mathrm{V}_{\mathrm{g}}-\rho_{\mathrm{He}} \mathrm{V}_{\mathrm{g}}}{\rho_{\mathrm{air}} \mathrm{V}_{\mathrm{L}}}}$
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
- 1Acharged particle enters a uniform magnetic field perpendicular to its initial direction travelling in air. The path of the particle is seen to follow the path in figure. Which of statements $1-3$ is/are correct?View Solution
$[1]$ The magnetic field strength may have been increased while the particle was travelling in air
$[2]$ The particle lost energy by ionising the air
$[3]$ The particle lost charge by ionising the air
- 2To know the resistance $G$ of a galvanometer by half deflection method, a battery of $emf\, V_E$ and resistance $R$ is used to deflect the galvanometer by angle $\theta $. If a shunt of resistance $S$ is needed to get half deflection then $G, R$ and $S$ related by the equationView Solution
- 3Suppose an isolated north pole is kept at the centre of a circular loop carrying a electric current $i$. The magnetic field due to the north pole at a point on the periphery of the wire is $B$. The radius of the loop is $a$. The force on the wire isView Solution
- 4In an experiment, electrons are accelerated, from rest, by applying, a voltage of $500 \,V.$ Calculate the radius of the path if a magnetic field $100\,mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19}\,C$ Mass of the electron $= 9.1 \times 10^{-31}\,kg$ ]View Solution
- 5Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length $25\,cm$ isView Solution
- 6A straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is$......$View Solution
- 7An electron is moving on a circular path of radius $r$ with speed $v$ in a transverse magnetic field $B$. $e/m$ for it will beView Solution
- 8In figure two parallel infinitely long current carrying wires are shown. If resultant magnetic field at point $A$ is zero. Then determine current $I.$ (in $A$)View Solution
- 9A galvanometer of resistance $50\, \Omega$ is connected to a battery of $3\, V$ along with a resistance of $2950\, \Omega$ in series. A full scale deflection of $30$ divisions is obtained in the galvanometer. In order to reduce this deflection to $20$ divisions, the resistance in series should be.......$Ω$View Solution
- 10Rank the value of $\oint {\vec B.\overrightarrow {dl} } $ for the closed paths shown in figure from the smallest to largestView Solution
