Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
A particle is acted upon by a force given by $F=-\alpha x^{3}-\beta x^{4}$ where $\alpha$ and $\beta$ are positive constants. At the point $\mathrm{x}=0$, the particle is $-$
PhysicsCenter of Mass Momentum and CollisionKVPYKVPY 2012 (SB/SX)
Options:
  • A In stable equilibrium
  • B In unstable equilibrium
  • C In neutral equilibrium
  • D Not in equilibrium
Solution:
2634 Upvotes Verified Answer
The correct answer is: In neutral equilibrium
$\frac{-\mathrm{d} \mathrm{U}}{\mathrm{dx}}=\mathrm{F},\left(\frac{\mathrm{d} \mathrm{U}}{\mathrm{dx}}\right)_{\mathrm{x}=0}=0 \text { and }\left(\frac{\mathrm{d}^{2} \mathrm{U}}{\mathrm{dx}^{2}}\right)_{\mathrm{x}=0}=0$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.