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A block and tackle system has $5$ pulleys. If an effort of $1000\,N$ is needed in the downward direction to raise a load of $4500\,N$. Calculate the efficiency of the system.
A) $80\% $
B) $90\% $
C) $50\% $
D) $60\% $

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Last updated date: 19th Jul 2024
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Answer
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Hint: Here we have to apply the concept of velocity lever and how load, effort and tension works in machines. The velocity ratio indicates the distance travelled by the pulley.

Complete step by step answer:
Velocity ratio is the ratio of the length of the out-lever to the in-lever (length of the resistance arm over stress arm). In order to increase the velocity ratio of the load being moved, we have to increase the resistance arm by bringing the fulcrum closer to the effort. Since, the velocity ratio or ideal mechanical advantage is a basic ratio of two lengths, the velocity ratio does not have any units. There is no work of friction here.

The machine generates force and regulates the direction and motion of force but it cannot generate energy. The capacity of a machine to do work is calculated by two variables.
They are –mechanical advantages and efficiency.
The mechanical advantage of a lever is given by load over effort.
Less effort is needed to do a job if the effort lever is longer.

The work efficiency formula is efficiency equals output over input and we can multiply the outcome by $100$ to obtain work efficiency as a percentage. This is used in various ways of calculating energy and work, whether it is energy generation or machine efficiency.
Tension levers are somewhat similar to flexible handles, allowing regular adjustment and quick clamping.
Velocity ratio of the lever is $5$ meaning the effort distance of the lever is $5$ times the effort distance of the load.
We know that efficiency of a pulley is given by:
$\eta = \dfrac{{{\text{mechanical}}\,{\text{advantage}}}}{{{\text{velocity}}\,{\text{ratio}}}}$

So, the mechanical advantage is given by:
$
M.A = \dfrac{{load}}{{effort}} \\
   = \dfrac{{4500}}{{1000}} \\
   = 4.5 \\
$
Velocity ratio $ = $ number of pulleys used $ = 5$
Therefore, efficiency
$
\eta = \dfrac{{4.5}}{5} \times 100\% \\
   = 90\% \\
 $
Hence, option (B) is correct.

Note: Here five pulleys are drawn since the velocity ratio is five. So, we have to see what the number of the velocity ratio is.