2. Please explain the answer. The graph represents the potential energy U as a function of position r for a particle of mass m. If the particle isreleased from rest at position rọ, what will its speed be at position 3ro? (Note in the proposed answers, sqrt meansUſr)3U02U0Uoro2ro3ro4rosgrt(2 UO /m)The particle will never reach position 3 ro.O sqrt(8 UO /m)O sqrt(4 UO /m)O sqrt(6 UO /m)

Name: 2. Please explain the answer. The graph represents the potential energ
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: 2. Please explain the answer. The graph represents the potential energy U as a function of position r for a particle of mass m. If the particle isreleased from rest at position rọ, what will its speed be at position 3ro? (Note in the proposed answers

Given: The potential energy is U. The position is r. The mass of the particle is m. The velocity of the particle at r=r0 will be zero that is v0=0 because it is given that the particle is at rest position. The expression from conservation of energy is given by, E+U=E'+U' Here, U is the potential energy at r0 whose value from graph is 3U0, U' is the potential energy at 3r0 whose value from graph is 2U0 and E' is the kinetic energy at 3r0.Substitute the values in the above expression. 12mv02+3U0=mv2+2U00+3U0=12mv2+2U0U0=12mv2v=2U0m Thus, the speed of the particle at 3r0 is v=2U0m and option (a) is the correct answer.