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Q.

Two uniform ropes A and B made of same material with different circular cross – sections are kept on a table such that a fraction of their lengths are hanging freely from the edge of the table. If the diameters of the ropes A and B are in the ratio 1:2 and their hanging lengths are in the ratio 2:1 respectively, the ratio of work done to pull the entire ropes A and B on the table is

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a

1 : 2

b

2 : 1

c

2 : 3

d

1 : 1

answer is D.

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Detailed Solution

The work done to pull the rope on the table
$= \frac{mgL}{2 n^{2}} = \frac{(ALp) gL}{2 {(\frac{L}{l})}^{2}} = \frac{{Apgl}^{2}}{2}$
$\begin{array}{l} ∴ {WαAl}^{2} {αD}^{2} l^{2} (l = hanging length) \\ \frac{W_{A}}{W_{B}} = {(\frac{D_{A}}{D_{B}})}^{2} x {(\frac{l_{A}}{l_{B}})}^{2} = 1 \end{array}$

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