Question

A Particle of mass 100 gm moves in a potential well given by U = 8x² – 4x + 400 Joule. Find its acceleration at a distance of 25 cm from equilibrium in positive direction –

• A. 0
• B. 40 m/s²
• C. –40 m/s²
• D. 20 m/s²

Answer 1

Answer: (C)

–40 m/s²

Answer 2

F = = –(16x – 4) = 4 – 16x

At equilibirum 4 – 16x₀ = 0

and x₀ = $\frac { 1 } { 4 }$m = 25 cm.

At the given position x = (25 + 25) = 50 cm.

̃ F = 4 – 16 × .5 = –4 N.

or a = $\frac { - 4 } { 0.1 }$ = – 40 m/s²