Question

Which of the following shows motion in a straight line?
A. Train on straight bridge
B. Tree swaying
C. Child on merry-go-round
D. none of these

Answer 1

In order to solve this question, we will use the definition of motion in a straight line according to which any motion can be regarded as a straight line if the path traced by particle depends on just one coordinate that is motion must be confined in one direction.Here the path traced means the locus of all points covered by the body.

Complete step by step answer:
Let us explore each and every options and try to find out which motion is in $1 - D$
Considering option A: Here we consider the bridge to be in some particular direction, say X-axis. So the train is going in only $x$ direction, that is motion is $1 - D$ So we can consider this motion as “Motion in Straight line “.

Considering option B: Here due to the swaying motion path traced by tree cannot be confined in one dimension rather it’s a $3 - D$ so Motion of Tree cannot be considered as motion in straight line.

Considering option C: As we know in a merry go round the body moves along a circle having a radius r and we knew from the circle equation ${x^2} + {y^2} = {r^2}$. That is motion is in $2 - D$ so motion here cannot be considered as a motion in a straight line.

Hence, the correct option is A.

Note: It should be remembered that, motion in $2 - D$ may or may not be a perfect circle rather ellipse but here in solution it is approximated as Circle if you consider it ellipse too then also motion is in $2$ dimension so you still get same answer . Also the coordinate considered in solution is randomly chosen as cartesian coordinate and in any random direction. You might consider the motion of the train in any direction X, Y or Z.