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Standard XII

Physics

Surface Energy

A given parti...

Question

A given particle starts at $x = 1$ on the potential function $U (x) = x^{2} - 10 x + 25$ , where $U$ is in Joules and $x$ is in meters. It then moves down the potential gradient to $x = 3$ where it has $4 J$ of potential energy. If it started at rest, how much kinetic energy does it have as it passes through $x = 3$ ?

2 J

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4 J

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8 J

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12 J

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16 J

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Solution

The correct option is C $12 J$
Potential energy function $U (x) = x^{2} - 10 x + 25$ J
Potential energy at $x = 1$ m, $U_{1} = 1^{2} - 10 (1) + 25 = 16$ J
Kinetic energy at $x = 1$ m, $K_{1} = 0$ J

Potential energy at $x = 3$ m, $U_{3} = 4$ J (given)
Using energy conservation: $U_{1} + K_{1} = U_{3} + K_{3}$
$∴$ $16 + 0 = 4 + K_{3}$ $⟹ K_{3} = 12$ J

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A given particle starts at x=1 on the potential function U(x)=x2−10x+25, where U is in Joules and x is in meters. It then moves down the potential gradient to x=3 where it has 4J of potential energy. If it started at rest, how much kinetic energy does it have as it passes through x=3?

The correct option is C 12JPotential energy function U(x)=x2−10x+25 JPotential energy at x=1 m, U1=12−10(1)+25=16 JKinetic energy at x=1 m, K1=0 JPotential energy at x=3 m, U3=4 J (given)Using energy conservation: U1+K1=U3+K3∴ 16+0=4+K3 ⟹K3=12 J