enEnglishguગુજરાતી
JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
If the potential energy between two molecules is given by \(U =\frac{-A }{ r ^{6}}+\frac{ B }{ r ^{12}},\) then at equilibrium, separation between molecules, and the potential energy are
- A \(\left(\frac{ B }{ A }\right)^{1 / 6}, 0\)
- B \(\left(\frac{ B }{2 A }\right)^{1 / 6},-\frac{ A ^{2}}{2 B }\)
- C \(\left(\frac{2 B }{ A }\right)^{1 / 6},-\frac{ A ^{2}}{4 B }\)
- D \(\left(\frac{2 B }{ A }\right)^{1 / 6},-\frac{ A ^{2}}{2 B }\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{2 B }{ A }\right)^{1 / 6},-\frac{ A ^{2}}{4 B }\)
Step-by-step Solution
Detailed explanation
\(U =\frac{- A }{ r ^{6}}+\frac{ B }{ r ^{12}}\) \(F =-\frac{ dU }{ dr }=-\left( A \left(-6 r ^{-7}\right)\right)+ B \left(-12 r ^{-13}\right)\) \(0=\frac{6 A }{ r ^{7}}-\frac{12 B }{ r ^{13}}\)…
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 pulley of radius \(1.5\,m\) is rotated about its axis by a force \(F =\left(12 t -3 t ^{2}\right)\,N\) applied tangentially (while \(t\) is measured in seconds). If moment of inertia of the pulley about its axis of rotation is \(4.5\,kg\,m ^{2}\), the number of rotations made by the pulley before its direction of motion is reversed, will be \(\frac{K}{\pi}\). The value of \(K\) is \(.....\)JEE Mains 2022 Hard
- If the distance between object and its two times magnified virtual image produced by a curved mirror is \(15 \mathrm{~cm}\), the focal length of the mirror must be _______.JEE Mains 2024 Hard
- The time period of a satellite, revolving above earth's surface at a height equal to \(R\) will be (Given \(g =\pi^2 m / s ^2, R =\) radius of earth)JEE Mains 2023 Medium
- In the figure shown below, a resistance of \(150.4 \Omega\) is connected in series to an ammeter A of resistance \(240 \Omega\). A shunt resistance of \(10 \Omega\) is connected in parallel with the ammeter. The reading of the ammeter is _____ mA.
JEE Mains 2025 Medium - Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statementJEE Mains 2026 Hard
- Two spherical bodies of same materials having radius 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is _________. (assume, effect of the surrounding temperature to be negligible),JEE Mains 2025 Hard
More PYQs from JEE Mains
- Let \(f\) be a differentiable function such that \(x ^2 f ( x )- x =4 \int \limits_0^x t f(t) d t, f(1)=\frac{2}{3}\).Then \(18 f(3)\) is equal to \(......\).JEE Mains 2023 Hard
- A cyclotron is used to accelerate protons. If the operating magnetic field is \(1.0\,T\) and the radius of the cyclotron 'dees' is \(60 cm\), the kinetic energy of the accelerated protons in \(MeV\) will be. [use \(m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C\) ]JEE Mains 2022 Medium
- A tangent to the curve, \(y\, = f(x)\) at \(P(x,y)\) meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\). If \(AP : BP\,= 1: 3\) and \(f(a)\, = 1\) , then the curve also passes through the pointJEE Mains 2017 Hard
- The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______.JEE Mains 2024 Hard
- As shown in the figure, a network of resistors is connected to a battery of \(2\,V\) with an internal resistance of \(3\,\Omega\). The currents through the resistors \(R_4\) and \(R_5\) are \(I_4\) and \(I_5\) respectively. The values of \(I_4\) and \(I_5\) are :
JEE Mains 2023 Hard - The electric field at the point associated with a light wave is given by \(E=200\left[\sin \left(6 \times 10^{15}\right) t+\sin \left(9 \times 10^{15}\right) t\right] \,Vm ^{-1}\) Given : \(h=4.14 \times 10^{-15} \,eVs\) If this light falls on a metal surface having a work function of \(2.50 \,eV\), the maximum kinetic energy of the photoelectrons will be ........... \(eV\)JEE Mains 2022 Hard