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An open tank containing liquid is moving with an acceleration on an inclined plane. The inclination of the free surface of the liquid will be __________ to the acceleration of the tank.
  • a)
    equal to
  • b)
    directly proportional
  • c)
    inversely proportional
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
An open tank containing liquid is moving with an acceleration on an in...
**Explanation:**

When a tank containing liquid is moving with an acceleration on an inclined plane, the inclination of the free surface of the liquid will be directly proportional to the acceleration of the tank. This can be explained by considering the forces acting on the tank and the liquid inside it.

**1. Forces acting on the tank:**
- Weight of the tank (Wt): This force acts vertically downwards and is given by Wt = mass of the tank x acceleration due to gravity.
- Normal force (Nt): This force acts perpendicular to the inclined plane and counteracts the weight of the tank.
- Frictional force (Ft): This force acts parallel to the inclined plane and opposes the motion of the tank.

**2. Forces acting on the liquid:**
- Weight of the liquid (Wl): This force acts vertically downwards and is given by Wl = mass of the liquid x acceleration due to gravity.
- Pressure forces (Pl): These forces act perpendicular to the free surface of the liquid and depend on the depth of the liquid.

**3. Effects of acceleration:**
When the tank accelerates, the liquid inside it also experiences an acceleration. This acceleration causes a relative motion between the liquid and the tank, leading to a sloping free surface of the liquid.

**4. Inclination of the free surface:**
The inclination of the free surface of the liquid is directly proportional to the acceleration of the tank. This can be understood by considering the pressure forces acting on the liquid. As the tank accelerates, the liquid is pushed towards the rear end of the tank, resulting in a higher pressure at the rear end compared to the front end. This pressure difference causes the free surface of the liquid to slope downwards towards the rear end.

Therefore, the inclination of the free surface of the liquid is directly proportional to the acceleration of the tank. As the acceleration increases, the inclination of the free surface also increases, and vice versa. Hence, the correct answer is option B: directly proportional.
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An open tank containing liquid is moving with an acceleration on an inclined plane. The inclination of the free surface of the liquid will be __________ to the acceleration of the tank.a)equal tob)directly proportionalc)inversely proportionalCorrect answer is option 'B'. Can you explain this answer?
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