A rope lies on a table such that a part of it hangsdown the table. Whe

1.	A rope lies on a table such that a part of it hangsdown the table. When the length of hanging part is1/3 of entire length the rope just begins to slide.The coefficient of friction between the rope andthe table is :
Answer» Let the total length of the rope be 'L' and m be the mass per unit length. Length of hanging rope 'L₂' = (1/3)L Mass of hanging rope 'M₂' = (1/3)L× m Length of the rope on the table 'L₁' = L - (1/3) L = (2/3)L Mass of the rope on the table 'M₁' = (2/3)L× m To find: Coefficient of friction between the rope and table. Let 'μ' be the coefficient of friction between the rope and table. Apply the motion of equation, The weight of rope on the table = The weight of hanging rope or, μ (2/3)L× mg = (1/3) L × mg or, μ = 1/2 = 0.5 Hence, the required coefficient of friction between the rope and table will be 0.5

A rope lies on a table such that a part of it hangsdown the table. When the length of hanging part is1/3 of entire length the rope just begins to slide.The coefficient of friction between the rope andthe table is :

Answer»

Let the total length of the rope be 'L' and m be the mass per unit length.

Length of hanging rope 'L₂' = (1/3)L

Mass of hanging rope 'M₂' = (1/3)L× m

Length of the rope on the table 'L₁' = L - (1/3) L = (2/3)L

Mass of the rope on the table 'M₁' = (2/3)L× m

To find: Coefficient of friction between the rope and table.

Let 'μ' be the coefficient of friction between the rope and table.

Apply the motion of equation,

The weight of rope on the table = The weight of hanging rope

or, μ (2/3)L× mg = (1/3) L × mg

or, μ = 1/2 = 0.5

Hence, the required coefficient of friction between the rope and table will be 0.5

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