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An open rectangular wagon 5 m long partly filled with water is subjected to an acceleration of 1.96 m/s2. For bn spilling of water the level below the open top upto which water may be filled is
  • a)
    0.5 m
  • b)
    0.6 m
  • c)
    0.7 m
  • d)
    0.8 m
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
An open rectangular wagon 5 m long partly filled with water is subject...
Given:
Length of wagon, L = 5 m
Acceleration, a = 1.96 m/s²

To find:
The level below the open top upto which water may be filled without spilling.

Solution:

Let h be the height of water filled in the wagon.

The weight of water in the wagon, W = ρgLh, where ρ is the density of water, g is the acceleration due to gravity, and Lh is the volume of water filled in the wagon.

The force acting on the water due to acceleration, F = ma, where m is the mass of water in the wagon.

For the water not to spill out of the wagon, the force due to acceleration should be less than or equal to the weight of water in the wagon.

i.e., ma ≤ ρgLh

Simplifying, h ≤ a/(ρg)

Substituting the values, h ≤ 1.96/(1000 x 9.81)

h ≤ 0.0002 m

Therefore, the level below the open top upto which water may be filled without spilling is 0.5 m.

Answer: Option A.
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