The given figure shows a block and tackle system of pulleys used to lift a load. When the load is pulled up by a distance 1 m, how far does the effort end move?

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Solution

The correct option is D
4m

Given displacement of load $d_{L} = 1 m$

Number of strands supporting the load = number of pulleys,(n) = 4

$M . A = \frac{L o a d}{E f f o r t} = \frac{n T}{T} = \frac{4 T}{T} = 4$

In a system of n pulleys, if the load moves up through a distance of d, each segment of the string supporting the load is loosened by a length d, so the effort arm moves through a distance 'nd'.

i.e., If $d_{L} = d$ and $d_{E} = n d$

Here, $d_{L} = 1 m$ then $d_{E} = 4 \times 1 = 4 m$

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