The potential energy function (in J) of a particle in a region of space is given as $\mathrm{U}=\left(2 \mathrm{x}^{2}+3 \mathrm{y}^{3}+2 \mathrm{z}\right)$. Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point $\mathrm{P}(1,2,3) \mathrm{m}$ is:

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Work, Power & Energy

The potential energy function (in J) of a particle in a region of space is given as

U = (2 x^{2} + 3 y^{3} + 2 z)

. Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point

P (1, 2, 3) m

is:

(A)2
(B)6
(C)4✓ Correct
(D)8

Answer: (C)

Solution

U = 2 x^{2} + 3 y^{3} + 2 z, F_{x} = - \frac{\partial U}{\partial x} = - 4 x

x = 1

∣ F_{x} ∣ = 4 N

.

Key confirmed: C.

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Work, Power & Energy →

More JEE Main questions on Work, Power & Energy

Given below are two statements:
Statement I: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $F$ . The work done by the force is $W = - \int_{r_{1}}^{r_{2}} F \cdot d r$ .
Statement II: Any object moving from one l …
JEE Main 2026View solution →
Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$ . Their centers have an initial separation of $4 R$ . Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$ , so that they can just touch e …
JEE Main 2026View solution →
A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 m / s^{2}$ , $β = 1 m / s$ an …
JEE Main 2026View solution →
In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30° shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)
JEE Main 2026View solution →
A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is $____$ N.
JEE Main 2026View solution →
A 1 kg block subjected to two simultaneous forces $(2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ N and $(3 \hat{i} - \hat{j} - 2 \hat{k})$ N is moved a distance of 25 m along $(3 \hat{i} - 4 \hat{j})$ direction. The work done in this process is _____ J.
JEE Main 2026View solution →