Question

In a lifting machine, an effort of $500N$ is to be moved by a distance of $20m$ to raise a load of $10000N$ by a distance of $0.8m$. Calculate the velocity ratio and mechanical advantage?
$\begin{array}{rl}& A.10\text{ and }35\\ & B.20\text{ and }35\\ & C.10\text{ and }25\\ & D.25\text{ and }20\end{array}$

Answer 1

Hint: The velocity ratio can be found by taking the ratio of the distance moved by effort to the distance moved by the load. The mechanical advantage is given by taking the ratio of the weight of the load to the weight of the effort. First of all find the velocity ratio and then mechanical advantage. These all will help you in solving out this question.

Complete step by step answer:
The velocity ratio can be found by the ratio of the distance moved by effort to the distance moved by the load. This can be expressed as an equation,
$V_R={\displaystyle \frac{E_d}{L_d}}$
It has been already mentioned in the question that the distance moved by the effort will be,
$E_d=20m$
And the distance moved by the load can be written as,
$L_d=0.8m$
Therefore we can substitute this in the equation of velocity ratio. That is,
$\begin{array}{rl}& V_R={\displaystyle \frac{E_d}{L_d}}={\displaystyle \frac{20}{0.8}}\\ & V_R=25\end{array}$
Now let us find out the mechanical advantage of the machine,
It is found by the ratio of the weight of the load to the weight of the effort.
This can be expressed in an equation as,
$MA={\displaystyle \frac{\text{load}}{\text{effort}}}$
It has been mentioned in the question that the weight of the effort is given as,
$effort=500N$
And the weight of the load can be calculated as,
$load=10000N$
Substituting the values in the equation of mechanical advantage will give,
$MA={\displaystyle \frac{10000}{500}}=20$

So, the correct answer is “Option D”.

Note: Mechanical advantage is a quantity for the calculation of the force amplification produced by using a tool, mechanical device or machine system. An example for this is the law of the lever. Velocity ratio is the ratio of a distance through which a component of a machine moves to that which the driving component is moving during the identical time.