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Question #42301

Difficulty: 8/10 | 🟢 Free

The Question

A smooth wedge of mass $M$ and angle $\theta$ rests on a smooth horizontal surface. The inclined surface faces right, meaning its height decreases towards the right. A small block of mass $m$ is placed on the incline. A horizontal force $F(t) = mg \sin\theta \cos\theta + c t$ (where $c$ is a positive constant and $t$ is time) is applied to the wedge towards the left. If the system starts from rest at $t=0$ , which of the following expressions gives the relative velocity of the block with respect to the wedge down the incline as a function of time $t$ ?

Options

A.
$gt \sin\theta + \frac{ct^2 \cos\theta}{2(M + m \sin^2\theta)}$
B.
$gt \sin\theta + \frac{ct^2 \cos\theta}{2M}$
C.
$gt \sin\theta + \frac{ct^2 \cos\theta}{2(M + m)}$
D.
$gt \sin\theta$

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

Wedge Constraint Logic|Relative Velocity in 2D|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly formulate constraint equations and equations of motion in a non-inertial frame with time-varying forces.

The primary trap lies in the normal force coupling: students frequently assume $N = mg\cos\theta$ , forgetting that the wedge's acceleration introduces a pseudo-force component $ma_w\sin\theta$ normal to the surface.

This omission leads to an incorrect effective mass of the system in the differential equation.

Furthermore, the time-varying force prevents the use of standard constant-acceleration kinematics, forcing students to correctly integrate the second-order derivative of the relative displacement vector.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Wedge Constraint Logic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free