Before You Begin

Question #42394

Difficulty: 8/10 | 🟢 Free

The Question

A uniform cubical block of mass $m$ and side $a$ rests on a rough horizontal surface. The coefficients of static and kinetic friction between the block and the surface are $\mu_s = 0.4$ and $\mu_k = 0.3$ , respectively. A horizontal force $F(t) = kt$ (where $k$ is a positive constant and $t$ is time) is applied horizontally at the top edge of the block. Find the magnitude of the linear momentum of the block at the exact instant it begins to topple. Assume acceleration due to gravity is $g$ .

Options

A.
$\frac{3 m^2 g^2}{40 k}$
B.
$\frac{m^2 g^2}{25 k}$
C.
$\frac{3 m^2 g^2}{200 k}$
D.
$\frac{49 m^2 g^2}{200 k}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Toppling vs Sliding|Variable Force Integration|Motion in a Plane

Why This Question Is Tricky

Common Mistakes

This question tests the interplay between translational dynamics and rotational equilibrium in a non-inertial frame.

A common trap is assuming the toppling condition remains $F \cdot a = mg \cdot a/2$ (yielding $F = 0.5mg$ ) even after the block starts sliding.

Students must recognize that once sliding begins, the kinetic friction $f_k$ provides an additional overturning torque about the center of mass (or equivalently, the pseudo force must be included if taking torque about the accelerating bottom edge).

This shifts the toppling threshold to $F = mg(1 - \mu_k)$ .

Furthermore, the momentum calculation requires integrating the net force only over the time interval after static friction is overcome.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	System of Particles and Rotational Motion - Class 11 Part 1
Concept	Toppling vs Sliding
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free