Question

The potential energy of a particle is given by formula $U=100-5x+100x^2$, U and x are in SI units if mass of the particle is 0.1 kg then magnitude of it's acceleration.

• A. At 0.05 m from the origin is $50m/s^2$
• B. At 0.05 m from the mean position is $100m/s^2$
• C. At 0.05 m from the origin is $150m/s^2$
• D. At 0.05 m from the mean position is $200m/s^2$

Answer 1

The correct option is A At 0.05 m from the origin is $50m/s^2$

Force is $F=\frac{-dU}{dx}=0-5+200x=200x-5$

Put $x=0.05m$ we get force as $F=5Newton$

So acceleration, $a=Force/mass=5/0.1=50m/s^2$

Option A is correct.