Before You Begin

Question #42395

Difficulty: 8/10 | 🟢 Free

The Question

A uniform rectangular block of mass $m$ , height $h$ , and base width $b$ is released from rest on an inclined plane making an angle $\theta$ with the horizontal. A thin layer of fluid on the incline exerts a viscous drag force on the block of magnitude $F_v = kv$ directed up the incline, where $v$ is the instantaneous velocity of the block and $k$ is a positive constant. The drag force acts uniformly over the bottom face of the block. Given that $\tan\theta > \frac{b}{h}$ , the block will eventually topple forward. Find the time $t$ after release at which the block begins to topple.

Options

A.
$\frac{m}{k} \ln\left( \frac{h \tan\theta}{h \tan\theta - b} \right)$
B.
$\frac{m}{k} \ln\left( \frac{h \tan\theta}{h \tan\theta + b} \right)$
C.
$\frac{m}{k} \ln\left( \frac{b \tan\theta}{b \tan\theta - h} \right)$
D.
$\frac{m}{k} \ln\left( \frac{h \sin\theta}{h \sin\theta - b} \right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Toppling vs Sliding|Viscosity and Stokes' Law|Work, Energy, and Power

Why This Question Is Tricky

Common Mistakes

Students often incorrectly assume that the normal force always acts through the center of mass, or they calculate torques about the toppling edge but forget to account for the non-inertial pseudo force (or the rate of change of angular momentum in the lab frame) due to the block's acceleration.

By placing the velocity-dependent drag force at the bottom face, the problem forces students to recognize that the drag induces a tipping torque about the center of mass.

This torque must be balanced by a forward shift in the normal force's line of action.

The trap is failing to couple the rotational equilibrium condition (which gives a critical velocity for toppling) with the translational first-order differential equation (which gives velocity as a function of time).

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