1.

The potential energy of a particle of mass `m` free to move along the x-axis is given by `U=(1//2)kx^2` for `xlt0` and `U=0` for `xge0` (x denotes the x-coordinate of the particle and k is a positive constant). If the total mechanical energy of the particle is E, then its speed at `x=-sqrt(2E//k)` isA. (a) ZeroB. (b) `sqrt((2E)/(m))`C. (c) `sqrt(E/m)`D. (d) `sqrt((3E)/(2m))`

Answer» Correct Answer - A
From the conservation of energy
`KE+PE=E` or `KE=E-1/2kx^2`
`KE` at `x=-sqrt((2E)/(k))` is `E-1/2k((2E)/(k))=0`
The speed of particle at `x=-sqrt((2E)/(k))` is zero.


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