A uniform vertical electric field E is established in the space b… - Vidyadip

MCQ

A uniform vertical electric field $E$ is established in the space between two large parallel plates. A small conducting sphere of mass $m$ is suspended in the field from a string of length $L$. If the sphere is given $a + q$ charge and the lower plate is charged positvely, the period of oscillation of this pendulum is :-

A
${2\pi }\sqrt[]{{\frac{L}{g}}}$
B
${2\pi }\sqrt[]{{\frac{L}{{g + (qE/m)}}}}$
✓
${2\pi }\sqrt[]{{\frac{L}{{g - (qE/m)}}}}$
D
${2\pi }\sqrt[]{{\frac{L}{{{{\left[ {{g^2} - {{(qE/m)}^2}} \right]}^{\frac{1}{2}}}}}}}$

✓

Answer

Correct option: C.

${2\pi }\sqrt[]{{\frac{L}{{g - (qE/m)}}}}$

c
The equation of motion of sphere, $m a=m g-q E \Rightarrow a=g-\frac{q E}{m}$

Thus the effective acceleration of sphere oscillation will become$:$ $g^{\prime}=a=g-\frac{q E}{m}$

Time period, $T=2 \pi \sqrt{\frac{L}{g^{\prime}}}=2 \pi \sqrt{\frac{L}{g-\frac{q E}{m}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 1. Electric charges and fields→1. Electric charges and fields — all question types→Physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

A circuit to verify $Ohm's$ law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit

An object is placed first at infinity and then at $20 cm$ from the object side focal plane of the convex lens. The two images thus formed are $5 cm$ apart. The focal length of the lens is......$cm$

In an $LCR$ circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of $220\ V$ and $100\ Hz$ is connected to it as shown ?

Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V=10$ axy

The temperature of an ideal gas in $3-$dimensions is $300\, {K}$. The corresponding de-Broglie wavelength of the electron approximately at $300\,{K}$, is $....\,nm$

$\left\lfloor{m}_{e}=\text { mass of electron }=9 \times 10^{-31} \,{kg}\right.$

${h}=\text { Planck constant }=6.6 \times 10^{-34} {Js}$

$\left.{k}_{{B}}=\text { Boltzmann constant }=1.38 \times 10^{-23}\, {JK}^{-1}\right]$

In a circuit consisting of a capacitance and a generator with alternating emf $E_{g}=E_{g0}$ $sin\omega t,$ $V_{C}$ and ${I}_{{C}}$ are the voltage and current. Correct phasor diagram for such circuit is :

The current in a coil of inductance 5 H decreases at the rate of 2 A/s. The induced e.m.f. is

The capacitance of a parallel plate capacitor is 12μF. If the distance between the plates is doubled and area is halved, then new capacitance will be

Equal charges $q$ are placed at the four corners $A,\,B,\,C,\,D$ of a square of length $a$. The magnitude of the force on the charge at $B$ will be

Eddy currents are produced when