If the potential energy of the particle is given by: U = x^2-8x+16. It starts from rest from x=0. What will be its maximum speed during SHM? Assume the mass of the particle to be 1kg.(a) 4√2m/s(b) 8m/s(c) 2√2m/s(d) 2√6m/sThe question was asked during a job interview.The question is from Oscillations in division Oscillations of Physics – Class 11

If the potential energy of the particle is given by: U = x^2-8x+16. It

1.	If the potential energy of the particle is given by: U = x^2-8x+16. It starts from rest from x=0. What will be its maximum speed during SHM? Assume the mass of the particle to be 1kg.(a) 4√2m/s(b) 8m/s(c) 2√2m/s(d) 2√6m/sThe question was asked during a job interview.The question is from Oscillations in division Oscillations of Physics – Class 11
Answer» Correct CHOICE is (a) 4√2m/s The explanation is: F = -dU/dx = 8 – 2x. Particle STARTS from x=0, so force will increase its speed till force becomes zero at x=4. Let acceleration be ‘a’. a = dv/dt = v dv/dx. And a = F/m = F/1 = 8-2x. adx = vdv. Now, integrate both sides.The LIMITS of dx will be 0 to 4 and the limits of dv will be 0 to v. (8x – x^2)0^4 = v^2/2. ∴ v = 4√2 m/s.

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