A uniform cubical box of side a is placed on a rough floor and it is to be moved by applying minimum possible force F at a point which is at a distance b above its centre of mass. If the coefficient of friction is μ = 0 . 4 , then what is the maximum possible value of 100 × b a for which the box will not topple before moving?

Question

A uniform cubical box of side a is placed on a rough floor and it is to be moved by applying minimum possible force F at a point which is at a distance b above its centre of mass. If the coefficient of friction is μ = 0 . 4 , then what is the maximum possible value of 100 × b a for which the box will not topple before moving?,

MARKS App · Accepted Answer

For no toppling F a 2 + b ≤ m g a 2 ⇒ μ a 2 + μ b ≤ a 2 ⇒ 0 . 2 a + 0 . 4 b ≤ 0 . 5 a ⇒ 0 . 4 b ≤ 0 . 3 a ⇒ b ≤ 3 a 4 ⇒ b ≤ 0 . 75 a (in limiting case ) But it is not possible as maximum value of b can be equal to 0 . 5 a only ∴ 100 b a max = 50 . 00

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