A particle in a certain consevative force field has a potential energy given by U -20 xy - Z- The force exerted on it is 20 y - z -20 x - z -20 xy - z 2-20 y - z -20 x - z -20 xy - z 2 k-C- -20 y - z -20 x - z -20 xy - z 2 k-20 y - z -20 x - z -20 xy - z 2 k-

Given: U=2xyz For a conservative field, F= ∂ U∂ r Where, nbsp; ∴F= [ î∂ U∂ x+ĵ∂ U∂ y+k̂∂ U∂ z ] = [ î∂∂ x ( 20xyz )+ĵ∂∂ y ( 20xyz )+k̂∂∂ z ( 20xyz ) ] = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Conservative and Non Conservative Forces

A particle in...

Question

A particle in a certain consevative force field has a potential energy given by $U = \frac{20 x y}{z}$ . The force exerted on it is

(\frac{20 y}{z})^i + (\frac{20 x}{z})^j + (\frac{20 x y}{z^{2}})^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- (\frac{20 y}{z})^i - (\frac{20 x}{z})^j + (\frac{20 x y}{z^{2}})^k

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- (\frac{20 y}{z})^i - (\frac{20 x}{z})^j - (\frac{20 x y}{z^{2}})^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{20 y}{z})^i + (\frac{20 x}{z})^j - (\frac{20 x y}{z^{2}})^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $- (\frac{20 y}{z})^i - (\frac{20 x}{z})^j + (\frac{20 x y}{z^{2}})^k$
Given: $U = \frac{2 x y}{z}$
For a conservative field, $F = - \frac{\partial U}{\partial r}$
Where,
$∴ \to F = - [^i \frac{\partial U}{\partial x} +^j \frac{\partial U}{\partial y} +^k \frac{\partial U}{\partial z}]$
$= - [^i \frac{\partial}{\partial x} (\frac{20 x y}{z}) +^j \frac{\partial}{\partial y} (\frac{20 x y}{z}) +^k \frac{\partial}{\partial z} (\frac{20 x y}{z})]$
$= - [^i (\frac{20 y}{z}) + (\frac{20 x}{z})^j + (- \frac{20 x y}{z^{2}})^k]$
$= - (\frac{20 y}{z})^i - (\frac{20 x}{z})^j + (\frac{20 x y}{z^{2}})^k$
Hence, the correct answer is option (b).

Suggest Corrections

Similar questions

Q. A particle in a certain consevative force field has a potential energy given by

U = \frac{20 x y}{z}

. The force exerted on it is

Q. A particle in a certain conservative force field has a potential energy given by

U = \frac{20 x y}{z}

. The force exerted on it is?

Q. The electric field in a region is given by:

\to E = (4 a x y \sqrt{z})^i + (2 a x^{2} \sqrt{z})^j + (\frac{a x^{2} y}{\sqrt{z}})^k

, where

a

is a positive constant. The equation of an equipotential surface will be of the form

Q. Let

^i,^j,^k

be three mutually or orthogonal unit vectors and let

x, y, z

be three distinct real numbers. If the vectors

\to u = x^i + y^j + z^k, \to v = y^i + z^j + x^k

and

\to w = z^i + x^j + y^k

are coplanar then

5 x (4 x y + x y z)

= _____

Join BYJU'S Learning Program

A particle in a certain consevative force field has a potential energy given by U=20xyz. The force exerted on it is

A particle in a certain consevative force field has a potential energy given by $U = \frac{20 x y}{z}$ . The force exerted on it is