Before You Begin

Question #42464

Difficulty: 8/10 | 🟢 Free

The Question

A block of initial mass $m_0 = 10 \text{ kg}$ rests on a rough inclined plane angled at $\theta = 30^\circ$ to the horizontal. The coefficient of static friction is $\mu_s = 1/\sqrt{3}$ . The block is equipped with a pulse-jet that expels gas at a constant rate $\mu = 0.1 \text{ kg/s}$ with a relative exhaust velocity $u = 20\sqrt{3} \text{ m/s}$ . The jet provides a thrust force whose line of action is in the vertical plane containing the line of greatest slope, directed upwards and outwards at an angle $\alpha = 30^\circ$ relative to the incline. At what time $t$ does the block just begin to slide up the incline? (Take $g = 10 \text{ m/s}^2$ )

Options

A.
$96 \text{ s}$
B.
$97 \text{ s}$
C.
$98 \text{ s}$
D.
$100 - 2\sqrt{3} \text{ s}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Recoil and Thrust Forces|Kinetic Friction Transition|Frame of Reference|Vector Decomposition

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze a variable mass system coupled with state-dependent constraints (static friction).

The primary trap is the 'Dynamic Normal Force.' Students often mechanically write $N = mg \cos\theta$ and fail to account for two critical dynamic factors: (1) the mass $m(t)$ is continuously decreasing due to fuel expulsion, and (2) the thrust force has a perpendicular component that actively reduces the normal force.

Failing to subtract the perpendicular thrust component leads to an incorrect time of $97 \text{ s}$ , while adding it leads to $98 \text{ s}$ .

Solving this requires synthesizing kinematics, Newton's laws for variable mass, and rigorous vector resolution to find the exact bifurcation point of motion.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Recoil and Thrust Forces
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free