Question

potential energy of a particle is given by u = 3x +4y^2+5z^2
find the corresponding conservative force.​

Answer 1

for maths and science question use use doubtnut app you'll get you will get your answer

Answer 2

Force corresponding to potential energy is       F = -3(i) -8y(j) -10z (k)

Step by step explanation:

The relation between conservative  force and potential energy is ,

Force is the negative derivative of potential energy with respect to its position.

It means force increases as the distance deceases.

$\mathds{F} = \frac{-dU}{dx} i \frac{-dU}{dy} j\frac{-dU}{dz} k$                                                (equation (1))

U = 3x + 4y² + 5z²    (given)

On  partially differentiating U with x, y and z.

We get,

$\frac{-dU}{dx} = -3\\ \\\frac{-dU}{dy} = -8y \text{ and } \frac{-dU}{dz} = -10z$

Putting all the values in the formula of force,

We get

$\textbf{\Large F = -3(i) -8y(j) -10z (k) }$