Question

How much is the displacement in completing one round of circular playground having $7\;m$ radius?
A. $0\;m$
B. $7\;m$
C. $22\;m$
D. $15\;m$

Answer 1

In order to solve this question we must know the meaning of displacement, so in terms of mechanics displacement is defined as the measurement of the length of shortest path from the initial point and final point. In simple words we can say it is the shortest distance between the starting point and ending point in our path. So in the case of a circular path, the starting point and ending point lie on the same point if we move one round of it.

Complete step by step answer:
According to our question we are asked to find the displacement when we complete one round of a circular playground which has a radius of $7\;m$ radius, so in order to find our answer in this case we will understand displacement in some depth. As we discussed earlier, displacement is the measure of shortest distance between final and initial point in our path and with these it is a vector quantity also which means it is dependent on direction of our motion and also the magnitude.

Let’s understand it by below given figure,

A person starts its journey from point $A$ to $B$ and then to $C$ so here if we see total distance travelled by person is $8m + 6m = 14m$, now if we are asked what is the displacement in this case so according to our definition shortest distance initial and final point will be our displacement, which is nothing but the distance between point $A$ and point $C$ which is $10\;m$.

Now as we understand it let's move towards our question, considering a scenario according to our question a person in a circular playground of $7\;m$ radius start moving from point $A$ in order to complete one round as shown in below figure,

Now we can analyze that, a person who starts to move from point A in order to complete one round of this circular playground finally reaches the same point from where it starts its journey which is point A.

So from here we can say the initial point and final point in the case of a circular path lies on the same point if we make one complete round of it. So according to the definition of displacement the shortest distance between the initial point and final point in our case of a circular playground is $0\;m$. From the above discussion we can conclude that displacement in completing one round of a circular playground having $7\;m$ radius is $0\;m$.

Hence the final answer is option A.

Note: While solving this type of question we usually make mistakes in understanding the difference between distance and displacement. If we are asked to find the distance in this case of a circular playground we would find the total distance covered in one round which will come out equivalent to circumference of the playground. So make sure to check what is asked in question in order to avoid mistakes. And one thing to note is the unit of distance and displacement is metre.