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Figure shows a system of four pulleys. The upper two pulleys are fixed and the lower two are movable.

Figure shows a system of four pulleys. The upper two pulleys are fixed and the lower two are movable. Machines, Concise Physics Class 10 Solutions.

(a) Draw a string around the pulleys. Also show the point of application and direction in which the effort E is applied.

(b) What is the velocity ratio of the system?

(c) How are load and effort of the pulley system related?

(d) What assumption do you make in arriving at your answer in part (c)?

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Answer

(a) The diagram below shows the point of application and direction of the effort E:

Draw a string around the pulleys. Also show the point of application and direction in which the effort E is applied. Machines, Concise Physics Class 10 Solutions.

(b) As we know that in a system of 4 pulleys, if the load moves up through a distance d, each segment of the string is loosened by a length d so the effort end moves through a distance 4 times d.

Velocity ratio=dEdLVelocity ratio=4dd⇒Velocity ratio=4\text{Velocity ratio} = \dfrac{dE}{dL} \\[0.5em] \text{Velocity ratio} = \dfrac{4d}{d} \\[0.5em] \Rightarrow \text{Velocity ratio}= 4 \\[0.5em]

(c) As we know,

M.A.=LoadEffortM.A. = \dfrac{\text {Load}}{\text {Effort}} \\[0.5em]

As M.A. = n = 4

Substituting the values in the formula we get,

LoadEffort=4⇒Load=4×Effort\dfrac{Load}{Effort} = 4 \\[0.5em] \Rightarrow Load = 4 \times Effort

(d) Assumptions made are —

(i) There is no friction in the pulley bearings.

(ii) Weight of lower pulleys is negligible.

(iii) The effort is applied downwards.

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