The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle \theta. If the acceleration is a m/s2, what will be the slope of the free surface?

Answers (1)

Let us assume the tanker is pulled by a force F and it produces an acceleration in the forward direction. Let \deltam be the mass of a small element.  As the tanker is pulled forward and accelerates, the small element also experiences a force in the same direction. The inertia of rest makes the element to remain at rest and hence as the tank moves forward, the element moves backwards as a result of inertia.

Force acting on \deltam, F1 = \deltama in the backward direction

F2 = \deltamg which is in a vertically downward direction.

The normal reaction gets balanced by various components: \deltama \sin \theta from F1

The situation when there is a maximum angle inclination by the surface,

\delta ma \cos \theta = \delta mg \sin \theta

So required slope, \frac{\sin \theta }{\cos \theta}=\frac{a}{g}

So, \tan \theta=\frac{a}{g}

Most Viewed Questions

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions