A particle is moving in a region, where its potential energy U varies with co-ordinates x, y and z as U=a2x2+y2+z2, where a is a positive constant. The force acting on the particle is

for a conservative force field F=-dUdxi^+dUdyj^+dUdzk^ =-axi^+yj^+zk^

A particle is moving in a region, where its potential energy U varies with co-ordinates x, y and z as U=a2x2+y2+z2, where a is a positive constant. The force acting on the particle is

for a conservative force field F=-dUdxi^+dUdyj^+dUdzk^ =-axi^+yj^+zk^

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A particle is moving in a region, where its potential energy U varies with co-ordinates x, y and z as $U = \frac{a}{2} (x^{2} + y^{2} + z^{2})$ , where a is a positive constant. The force acting on the particle is

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$- a (x \hat{i} + y \hat{j} + z \hat{k})$

$(x \hat{i} + y \hat{j} + z \hat{k})$

$- 2 a (x \hat{i} + y \hat{j} + z \hat{k})$

$- \frac{a}{2} (x^{2} + y^{2} + z^{2})$

answer is A.

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Detailed Solution

for a conservative force field

$F = - [(\frac{d U}{d x}) \hat{i} + (\frac{d U}{d y}) \hat{j} + (\frac{d U}{d z}) \hat{k}] = - a [(x \hat{i} + y \hat{j} + z \hat{k})]$

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A particle is moving in a region, where its potential energy U varies with co-ordinates x, y and z as U=a2x2+y2+z2, where a is a positive constant. The force acting on the particle is

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A particle is moving in a region, where its potential energy U varies with co-ordinates x, y and z as $U = \frac{a}{2} (x^{2} + y^{2} + z^{2})$ , where a is a positive constant. The force acting on the particle is