Question

A force of \[2\text{ kg wt}\] is applied on an object of mass \[\text{10kg}\] . How much acceleration will be produced in that object, given \[\text{g=9}\text{.8m/se}{{\text{c}}^{\text{2}}}\] ?

Answer 1

Hint: We have been given the force being applied on the body and we have to calculate the acceleration of the object. We can use Newton’s second law of motion which states that the force applied on a body is equal to the product of its mass and acceleration. We haven’t been given the mass of the body but we can find it with the help of force given.

Complete solution:
The kilogram-weight is a non-standard gravitational metric unit of force. It is equal to the magnitude of the force exerted on one kilogram of mass in the standard gravitational field. That is, it is the weight of a kilogram under standard gravity. Therefore, \[1\text{ kg wt = 9}\text{.8 N}\] by definition.
Hence we can say that mass of the body \[(m)=10\text{ kg}\]
Force exerted on the body \[\text{(F)=2 kg wt=(2}\times \text{9}\text{.8)N=19N}\]
From Newton’s second law of motion, we have \[\text{F=m}\text{.a}\] where the meanings of the symbols have already been discussed
From the above equation, we can say that, acceleration of the object \[\text{(a)=}\dfrac{\text{F}}{\text{m}}\]
Substituting the values in the above equation, we get
\[\text{a=}\dfrac{19}{10}=1.9m/{{s}^{2}}\]

Thus, acceleration of \[1.9m/{{s}^{2}}\] is produced in the body.

Note: The force given to us was in the units of kilogram weight, which is a unit of force, but we always try to present our answers in terms of the standard unit of measurement. That is why we first converted the force into newton. If we had proceeded with the values given to us, we would have reached at the wrong answer even after applying the right formula. Also, take care of the fact that even though the force is given in kilogram weight, the value in kilograms does not represent the mass of the body.