JEE Mains · Physics · STD 12 - 1. Electric charges and fields
Two small spheres each of mass \(10 \,mg\) are suspended from a point by threads \(0.5 \,m\) long. They are equally charged and repel each other to a distance of \(0.20 \,m\). The charge on each of the sphere is \(\frac{ a }{21} \times 10^{-8} \, C\). The value of \(a\) will be ...... . \(\left[\right.\) Given \(\left.g=10 \,ms ^{-2}\right]\)
- A \(10\)
- B \(16\)
- C \(24\)
- D \(20\)
Answer & Solution
Correct Answer
(D) \(20\)
Step-by-step Solution
Detailed explanation
\(T \cos \theta= mg =10 \times 10^{-6} \times 10=10^{-4}\) \(T \sin \theta=\frac{9 \times 10^{9} \times q ^{2}}{0.04}= F\) \(\tan \theta==\frac{0.1}{\sqrt{0.24}}=\frac{ F }{ mg }\) \(q =\frac{2 \sqrt{10}}{3 \sqrt{\sqrt{24}}} \times 10^{-8}\)…
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
- A block moving horizontally on a smooth surface with a speed of \(40\, {ms}^{-1}\) splits into two equal parts. If one of the parts moves at \(60\, {ms}^{-1}\) in the same direction, then the fractional change in the kinetic energy will be \(x: 4\) where \(x=..... .\)JEE Mains 2021 Hard
- A block of mass \(1 \mathrm{~kg}\) is pushed up a surface inclined to horizontal at an angle of \(60^{\circ}\) by a force of \(10 \mathrm{~N}\) parallel to the inclined surface as shown in figure. When the block is pushed up by \(10 \mathrm{~m}\) along inclined surface, the work done against frictional force is _______. \(\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right]\)
JEE Mains 2024 Hard - For an \(RLC\) circuit driven with voltage of amplitude \(v_m\) and frequency \({\omega _0} = \frac{1}{{\sqrt {LC} }}\) the current exhibits resonance. The quality factor, \(Q\) is given by:JEE Mains 2018 Easy
- Zener breakdown occurs in a \(p-n\) junction having \(p\) and \(n\) both :JEE Mains 2021 Medium
- Two different adiabatic paths for the same gas intersect two isothermal curves as shown in\(P-V\) diagram. The relation between the ratio \(\frac{V_a}{V_d}\) and the ratio \(\frac{V_b}{V_c}\) is _______.
JEE Mains 2024 Hard - The density \(\rho\) of a uniform cylinder is determined by measuring its mass \(m\), length \(l\) and diameter \(d\). The measured values of \(m\), \(l\) and \(d\) are \(97.42 \pm 0.02\) g, \(8.35 \pm 0.05\) mm and \(20.20 \pm 0.02\) mm, respectively. Calculated percentage fractional error in \(\rho\) is _______.JEE Mains 2026 Medium
More PYQs from JEE Mains
- A moving coil galvanometer of resistance \(100 \Omega\) shows a full scale deflection for a current of 1 mA . The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA , is _________ \(\Omega\)JEE Mains 2026 Easy
- Assume that the displacement\((s)\) of air is proportional to the pressure difference \((\Delta p)\) created by a sound wave. Displacement\((s)\) further depends on the speed of sound \((v),\) density of air \((\rho)\) and the frequency \((f)\) If \(\Delta p \approx 10\, Pa , v \approx 300\, m / s , p \approx 1\, kg / m ^{3}\) and \(f \approx 1000 \,Hz\), then \(s\) will be the order of (take multiplicative constant to be \(1\) )JEE Mains 2020 Easy
- If the real part of the complex number \((1-\cos \theta+2 i \sin \theta)^{-1}\) is \(\frac{1}{5}\) for \(\theta \in(0, \pi)\), then the value of the integral \(\int_{0}^{\theta} \sin x \,d x\) is equal to:JEE Mains 2021 Hard
- If \(50\) Vernier divisions are equal to \(49\) main scale divisions of a travelling microscope and one smallest reading of main scale is \(0.5 \mathrm{~mm}\), the Vernier constant of travelling microscope is _______.JEE Mains 2024 Hard
- Let \([\bullet]\) be the greatest integer function. If \( \alpha=\int_{0}^{64}(x^{1/3}-[x^{1/3}])dx, \) then \( \frac{1}{\pi}\int_{0}^{\alpha\pi}(\frac{sin^{2}\theta}{sin^{6}\theta+cos^{6}\theta})d\theta \) is equal to ___ .JEE Mains 2026 Medium
- If the shortest distance between the lines \( \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(2+\lambda) \hat{\mathrm{i}}+(1-3 \lambda) \hat{\mathrm{j}}+(3+4 \lambda) \hat{\mathrm{k}}, \lambda \in \mathbb{R} \) \( \mathrm{L}_2: \overrightarrow{\mathrm{r}}=2(1+\mu) \hat{\mathrm{i}}+3(1+\mu) \hat{\mathrm{j}}+(5+\mu) \hat{k}, \mu \in \mathbb{R}\) is \(\frac{\mathrm{m}}{\sqrt{\mathrm{n}}}\), where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\), then the value of \(\mathrm{m}+\mathrm{n}\) equals:JEE Mains 2024 Hard