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

Byju's Answer

Standard XII

Physics

Conservative Force as Gradient of Potential

Potential ene...

Question

Potential energy $U (x)$ and associated force $F (x)$ bear the relation $F (x) = \frac{- d U (x)}{d x}$ . Dependence of potential energy of a two-particle system on the separation $x$ between them is shown in the following figure.

Which of the following graphs shows the correct variation of force $F (x)$ with $x$ ?

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

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

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

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

Open in App

Solution

The correct option is A
$F (x) = - d U (x) / d x = -$ slope of $U (x) - x$ curve.
Initially, slope is constant and positive until $x = a$ . So, force is constant (negative) till that point. After that the slope of $U - x$ curve becomes zero, so the force becomes zero after $x = a$ .

Option (a) matches this description.

Suggest Corrections

Similar questions

Q. Potential energy

U (x)

and associated force

F (x)

bear the relation

F (x) = \frac{- d U (x)}{d x}

. Dependence of potential energy of a two-particle system on the separation

x

between them is shown in the following figure.

Which of the following graphs shows the correct variation of force

F (x)

with

x

Q. Potential energy

U (x)

and associated force

F (x)

bear the relation

F (x) = \frac{- d U (x)}{d x}

. Dependence of potential energy of a two-particle system on the separation

x

between them is shown in the following figure.

Which of the following graphs shows the correct variation of force

F (x)

with

x

Q. A single conservative force F(x) acts on a

1.0 k g

particle that moves along the x-axis.The potential energy U(x) is given by

U (x) = 20 + (x - 2)^{2}

where

x

is in meters.At

x = 5.0 m

, the particle has a kinetic energy of

20 J

. What is the mechanical energy of the system?

Q. A plot of potential energy function

U (x) = k x^{2}

, where

x

is the displacement and

k =

constant is shown below. The correct conservative force function

F (x)

Q. A single conservative force

F (x)

acts on a

2.5 kg

particle that moves along

x -

axis. The potential energy

U (x)

is given by

U (x) = (10 + (x - 4)^{2})

where

x

is in meter. At

x = 6 m

, The particle has kinetic energy of

20 J

. What is mechanical energy of the system?

Join BYJU'S Learning Program

Potential energy U(x) and associated force F(x) bear the relation F(x)=−dU(x)dx. Dependence of potential energy of a two-particle system on the separation x between them is shown in the following figure. Which of the following graphs shows the correct variation of force F(x) with x?

The correct option is A F(x)=−dU(x)/dx=− slope of U(x)−x curve. Initially, slope is constant and positive until x=a. So, force is constant (negative) till that point. After that the slope of U−x curve becomes zero, so the force becomes zero after x=a. Option (a) matches this description.