Question

A force of 1 Kg Wt. acting on a body of mass 9.8 kg will produce an acceleration of,
A. $\text{1 m/}{{\text{s}}^{\text{2}}}$
B. $1/9.8\text{ m/}{{\text{s}}^{2}}$
C. $9.8\text{ m/}{{\text{s}}^{2}}$
D. $1\text{ cm/}{{\text{s}}^{2}}$

Answer 1

Hint: To answer this we should know what is kilogram weight and how it is related to newton and apply newton’s second law to find acceleration. A kilogram-weight is defined as the weight of a kilogram under standard gravity. From Newton’s second law we know that the force on a body is the product of mass of the body and its acceleration.

Complete step by step answer:
We usually refer to kilograms as a measure of mass. If a body is said to be 2 kg it means its mass is 2 kilograms. Coming to the concept of weight, weight is the force acting on a body at the earth’s surface. It is a product of mass times the acceleration due to gravity (g). Its unit is Newton (N).
So 1 Kg Wt is referred to as the force acting on a body of 1 Kg at the surface of earth. So how newton is that? Multiply 1 Kg by acceleration due to gravity (g), we will get the value in newton.
In 1 Kg Wt, the force acting on the body in the problem is 9.8N.
So according to Newton's second law, force acting on an object is mass times acceleration.
$\text{F}=\text{ma}$
$\Rightarrow \text{a}=\dfrac{\text{F}}{\text{m}}=\dfrac{9.8}{9.8}$
$\therefore \text{a}=1\text{ m/}{{\text{s}}^{2}}$
So the answer to the question is option (A) $1\text{ m/}{{\text{s}}^{2}}$.

Note: We can say that the kilogram-weight is the force acting on a mass due to the gravity of a planet. Kilogram-weight is not an SI unit of force. Newton is the SI unit of force.
Kilogram weight is used to denote the thrust produced by a rocket while it is launching. This unit is still used by China and European space organizations for their rocket launching.
Since the value of acceleration due to gravity (g) changes with planet to planet. So, the kilogram weight or kilogram-force changes with planet to planet for the same mass.