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The vertical height of an almirah is $ 2 \mathrm{m} $ , its base is a square of side length $ 0.4 \mathrm{m} $ and its mass is 200 kg. The maximum height from the floor at which a horizontal force 490 N should be applied on the almirah so that it does not tilt is:
(A) 0.6 m
(B) 0.8 m
(C) 1 m
(D) 1.2 m

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Last updated date: 13th Jun 2024
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Answer
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Hint
We know that a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), that is to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F. Force is the push or pull applied on an object. It can move a stationary object or stop a moving object. Force can also change the speed and direction of a moving object. When force is applied on an object, resulting in the movement of that object, work is said to be done. Based on this concept we have to solve this question.

Complete step by step answer
We can assume that,
the maximum height be $x$ m
Therefore, by equating Torques we get,
 $ \Rightarrow \mathrm{F} \times \mathrm{x}=\mathrm{mg} \times \dfrac{1}{2} $
The above equation equates to,
 $ \Rightarrow 490\times \text{x}=200\times 9.8\times \dfrac{0.4}{2} $
 $ \Rightarrow \text{x}=0.8\text{m} $
Therefore, the correct answer is Option (B).

Note
 It should be known to us that when two forces are the same strength but act in opposite directions, they are called balanced forces. Again, tug-of-war is a perfect example. If the people on each side of the rope are pulling with the same strength, but in the opposite direction, the forces are balanced. The result is no motion. If two individual forces are of equal magnitude and opposite direction, then the forces are said to be balanced. An object is said to be acted upon by an unbalanced force only when there is an individual force that is not being balanced by a force of equal magnitude and in the opposite direction.