Question

One slug is equivalent to 14.6kg. A force of 10 pound is applied on a body of 1kg. The acceleration of the body is?
A. $44.5\,m/s^2$
B. $4.448\,m/s^2$
C. $44.4\,ft/s^2$
D. None of these

Answer 1

Hint: There are different units of mass which have different standards of measurements. Here, pound is measured in terms of Newton such that; 1 pound is equivalent to 4.45 Newton. Using this relation we have to find the acceleration of the body of mass 1kg through Newton’s second law of motion.

Complete step by step answer:
 Here, it is given that the value of one slug is given as 14.6kg. Now, the force applied on a body of one kilogram is ten pounds. Now, to calculate the acceleration on the body of 1kg, first we will need to understand Newton's second law of motion. Newton’s second law says that the force applied on a body is equal to the product of the mass of the body and the acceleration of the body. Thus, from Newton’s law, we can deduce the following equation:
$F=ma$
Here, $F$ is the force on the body, $m$ is the mass of the body and $a$ is the acceleration of the body. Now, force of 10 pounds is applied, and the conversion of pound to Newton is given as below:
\[
10\,pound = 4.45\,Newton \times 10 \\
\Rightarrow 10\,pound = 44.5\,Newton = F \\
\]
Thus, the force is 44.5 Newton. Now, the acceleration of the body on a body of mass 1kg is
\[a = \dfrac{F}{m}
\Rightarrow a = \dfrac{{44.5}}{1}
\therefore a = 44.5\dfrac{m}{{{s^2}}}\]
Thus the acceleration of the body is \[44.5\dfrac{m}{{{s^2}}}\]

Thus option A is the correct answer.

Note: Here, it is also given that one slug is equivalent to 14.6 kg, and even though it was of no use in our method, we can also find the force acted on the body in terms of slug using this equivalence. Kilogram is the standard unit of mass, pound is the British unit of weight while the unit of slug is used in the fertilizer industry.