Question:medium
A particle moves along the x-axis under a force $ F(x) = 6x^2 $ N. The work done by this force in moving the particle from $ x = 1 \, \text{m} $ to $ x = 2 \, \text{m} $ is:
A particle moves along the x-axis under a force $ F(x) = 6x^2 $ N. The work done by this force in moving the particle from $ x = 1 \, \text{m} $ to $ x = 2 \, \text{m} $ is:
Show Hint
When force is a function of position, use definite integration:
\[
W = \int_{x_1}^{x_2} F(x)\,dx
\]
Updated On: Jan 13, 2026
- 14 J
- 18 J
- 24 J
- 28 J
Show Solution
The Correct Option is A
Solution and Explanation
The work done by the force $ F(x) = 6x^2 $ from $ x = 1 \, \text{m} $ to $ x = 2 \, \text{m} $ is calculated using the work integral: $ W = \int_{x_1}^{x_2} F(x) \, dx $.
Substituting the values: $ W = \int_{1}^{2} 6x^2 \, dx $.
Evaluating the integral: $ W = 6 \int_{1}^{2} x^2 \, dx = 6 \left[ \frac{x^3}{3} \right]_{1}^{2} $.
This simplifies to: $ W = 6 \left( \frac{2^3}{3} - \frac{1^3}{3} \right) = 6 \left( \frac{8}{3} - \frac{1}{3} \right) = 6 \left( \frac{7}{3} \right) $.
The final result is: $ W = 14 \, \text{J} $.
Therefore, the work done is 14 J.
Was this answer helpful?
1
Top Questions on work, energy and power
- A curve is given between the potential energy \(U\) of a particle and its position on the \(x\)-axis as shown. Given: \[ \tan\theta_1 = 1,\qquad \tan\theta_2 = 3,\qquad \tan\theta_3 = -\frac{1}{2} \] If \(F_{AB}\) is the force acting on the particle during motion from \(A\) to \(B\), similarly \(F_{BC}\), \(F_{CD}\) and \(F_{DE}\) are the forces during \(B\) to \(C\), \(C\) to \(D\) and \(D\) to \(E\) respectively, arrange the magnitudes of these forces in decreasing order.
- JEE Main - 2026
- Physics
- work, energy and power
- A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:
- JEE Main - 2026
- Physics
- work, energy and power
- Given below are two statements:
Statement I: An object moves from position \( \vec{r}_1 \) to position \( \vec{r}_2 \) under a conservative force field \( \vec{F} \). The work done by the force is \[ W = -\int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}. \]
Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2026
- Physics
- work, energy and power
- A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is :
- JEE Main - 2026
- Physics
- work, energy and power
- Want to practice more? Try solving extra ecology questions todayView All Questions