A particle of mass M moves along a horizontal x axis from x = 0 to x… | NEET 2026 (Re-neet)

Q1NEET 2026 · RE-NEETMedium

Work by a Variable Force

A particle of mass $M$ moves along a horizontal $x$ axis from $x = 0$ to $x = L$ . The coefficient of kinetic friction varies as a function of $x$ as $\mu_k(x) = \mu_0 - \alpha x$ , where $\mu_0, \alpha$ are constants of appropriate dimensions, so that $\mu_k(L) = 0$ . The total work done by the frictional force during the motion is $n\mu_0 MgL$ , where $g$ is the acceleration due to gravity. The value of $n$ is:

Show answer and solution

Answer: (a)

$\mu_k(L) = 0 \Rightarrow \alpha = \frac{\mu_0}{L}$
$W_f = -\int_0^L \mu_k Mg\,dx = -Mg\left[\mu_0 L - \frac{\alpha L^2}{2}\right] = -Mg\left[\mu_0 L - \frac{\mu_0 L}{2}\right]$
$W_f = -\frac{1}{2}\mu_0 MgL$ , magnitude $\frac{1}{2}\mu_0 MgL$
So the answer is (a) $n = \frac{1}{2}$ .

Report a mistake

More questions on Work by a Variable Force

A force F = α + β x² acts on an object in the x -direction. The work done by the force is…JEE Main 2025 (24 Jan, Shift 1)
A force f = x²yi + y²j acts on a particle in a plane x + y = 10. The work done by this…JEE Main 2025 (23 Jan, Shift 1)
An object moving along horizontal x -direction with kinetic energy 10 J is displaced…NEET 2024
A force F = (2 + 3x)i acts on a particle in the x direction where F is in newton and x is…JEE Main 2023 (11 Apr, Shift 1)
A force F = (5 + 3y²) acts on a particle in the y -direction, where F is in newton and y…JEE Main 2023 (1 Feb, Shift 2)
A block of mass 10 kg is moving along x -axis under the action of force F = 5x N. The…JEE Main 2023 (15 Apr, Shift 1)
A particle of mass 10 g moves in a straight line with retardation 2x, where x is the…JEE Main 2023 (6 Apr, Shift 1)
An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under…JEE Main 2023 (25 Jan, Shift 1)

Work by a Variable Force question from NEET 2026 (Re-neet)

More questions on Work by a Variable Force