Question

In a wheel axle arrangement, the radius of the wheel is 25 times more than the radius of an axle. Find the mechanical advantage of the machine.
(A) $20$
(B) $25$
(C) $30$
(D) $35$

Answer 1

Hint: The mechanical advantage of the wheel and axle can be found by taking the ratio of the radius of the wheel over the radius of the axle. The larger the mechanical advantage of the machine, the greater the force that the machine can output.

Formula used:
The mechanical advantage of the wheel and axle is given by,
$MA = \dfrac{{{R_W}}}{{{R_A}}}$
Where, $MA$ is the mechanical advantage, ${R_W}$ is the radius of the wheel, and ${R_A}$ is the radius of the axle.

Complete step by step answer:
Given that,
In a wheel axle arrangement, the radius of wheel is $25$ times more than the radius of an axle, ${R_W} = 25 \times {R_A}$
Now,
The mechanical advantage of the wheel and axle is given by,
$MA = \dfrac{{{R_W}}}{{{R_A}}}\,................\left( 1 \right)$
By substituting the value of the radius of the wheel which is given in the question in the equation (1), then the equation (1) is written as,
\[\Rightarrow MA = \dfrac{{25 \times {R_A}}}{{{R_A}}}\]
On canceling the same terms in the numerator and the denominator, then the above equation is written as,
\[\Rightarrow MA = 25\]

$\therefore$ The mechanical advantage of the wheel axle is 25. Hence, option (B) is correct.

Note:
The ideal mechanical advantage of a wheel and axle is the ratio of the radii. If the effort is applied to the large radius, the mechanical advantage which will be more than one; if the effort is applied to the small radius, the mechanical advantage is which will be less than 1.