WBJEE · Physics · Oscillations
The bob of a pendulum of mass \(m\), suspended by an inextensible string of length \(L\) as shown in the figure carries a small charge \(a\). An infinite horizontal plane conductor with uniform surface charge density \(\sigma\) is placed below it. What will be the time period of the pendulum for small amplitude oscillations?
- A \(2 \pi \sqrt{\frac{\mathrm{L}}{\left(\mathrm{g}-\frac{\mathrm{mq}}{\varepsilon_{0} \sigma}\right)}}\)
- B \(\sqrt{\frac{\mathrm{L}}{\left(\mathrm{g}-\frac{\mathrm{mq} \sigma}{\varepsilon_{0}}\right)}}\)
- C \(\frac{1}{2 \pi} \sqrt{\frac{\mathrm{L}}{\left(\mathrm{g}-\frac{\mathrm{q} \sigma}{\varepsilon_{0} \mathrm{~m}}\right)}}\)
- D \(2 \pi \sqrt{\frac{\mathrm{L}}{\left(\mathrm{g}-\frac{\mathrm{q} \sigma}{\varepsilon_{0} \mathrm{~m}}\right)}}\)
Answer & Solution
Correct Answer
(D) \(2 \pi \sqrt{\frac{\mathrm{L}}{\left(\mathrm{g}-\frac{\mathrm{q} \sigma}{\varepsilon_{0} \mathrm{~m}}\right)}}\)
Step-by-step Solution
Detailed explanation
\(\therefore\) Apparent weight of the bob, \(w^{\prime}=m g-q E\) \[ m y^{\prime}=m g-q E \] \(\therefore\) \(g^{\prime}=g-\frac{q E}{m}\) Time period of a pendulum. \(T=2 \pi \sqrt{\frac{L}{g_{e f f}}}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two equal resistances, \(400 \Omega\) each, are connected in series with a \(8 \mathrm{V}\) battery. If the resistance of first one increases by \(0.5 \%\), the change required in the resistance of the second one in order to keep the potential difference across it unaltered is toWBJEE 2016 Medium
- The ionization energy of hydrogen is \(13.6 \mathrm{eV}\). The energy of the photon released when an electron jumps from the first excited state \((n=2)\) to the ground state of a hydrogen atom isWBJEE 2014 Easy
- The fundamental frequency of a closed pipe is equal to the frequency of the second harmonic of an open pipe. The ratio of their lengths isWBJEE 2013 Easy
-
What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figure?WBJEE 2020 Hard - Light of wavelength \(6000 Ã…\) is incident on a thin glass plate of \(\mu = 1.5\) such that the angle of refraction into the plate is \(60^{\circ}\). Calculate the smallest thickness of the plate which will make dark fringe by reflected beam interference.WBJEE 2024 Medium
- A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2000 times heavier than an electron, what will be the relation between the de Broglie wavelength of the proton \(\left(\lambda_{p}\right)\) and that of electron \(\left(\lambda_{c}\right) ?\)WBJEE 2019 Medium
More PYQs from WBJEE
- The number of diagonals in a polygon is 20 . The number of sides of the polygon isWBJEE 2011 Medium
- If \(x=1+\frac{1}{2 \times 1 !}+\frac{1}{4 \times 2 !}+\frac{1}{8 \times 3 !}+\ldots\) and
\(y=1+\frac{x^{2}}{1 !}+\frac{x^{4}}{2 !}+\frac{x^{6}}{3 !}+\ldots\)
Then, the value of loge \(y\) isWBJEE 2013 Medium - A weak acid of dissociation constant \(10^{-5}\) is being titrated with aqueous \(\mathrm{NaOH}\) solution. The \(\mathrm{pH}\) at the point of one-third neutralisation of the acid will beWBJEE 2010 Hard
- The line \(A A^{\prime}\) is on charged infinite \(A\) conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of charge \(\sigma\) and \(B\) is ball of mass \(m\) with a like charge of magnitude \(q . B\) is connected by string from a point on the line \(A A^{\prime}\). The tangent of angle (0) formed between the line \(A A^{\prime}\) and the string is
WBJEE 2015 Hard - A solution is saturated with \(\mathrm{SrCO}_{3}\) and \(\mathrm{Sr} \mathrm{F}_{2}\). The \(\left[\mathrm{CO}_{3}^{2-}\right]\) is found to be \(1.2 \times 10^{-3} \mathrm{M}\). The concentration of \(\mathrm{F}\) - in the solution would beWBJEE 2020 Hard
- In \(\triangle A B C\), co-ordinates of \(A\) are \((1,2)\) and the equation of the medians through \(B\) and \(C\) are \(x+y=5\) and \(x=4\) respectively. Then the midpoint of \(B C\) isWBJEE 2024 Medium