Question

Which of the following is true for displacement?
(a) it cannot be zero
(b) its magnitude is greater than the distance travelled by the object
(c) displacement may or may not be equal to distance.

A) (a) only
B) (b) and (c)
C) (c) only
D) All (a), (b) and (c)

Answer 1

Hint: Displacement is the length of the shortest straight line path distance between two points A and B, which may or may not be the same point.

Complete step by step answer:

Displacement refers to the length of the shortest straight line path connecting two points A and B, which may or may not be the same.
On the other hand, distance refers to the length of the actual path taken by a body in travelling from A to B.
It may be possible that the body moves from A to B in a curved path in which case the length of the path travelled by the body will be more than the straight line joining A and B (which is in fact, the displacement).

Hence, while moving from one point to another, the magnitude of the displacement of a body can never be more than the distance covered by it. The displacement and distance covered by the body can be equal only if the path taken by the body is a direct straight line between the two points.
If the two points A and B are the same point, then the shortest line between the two points is actually a zero point, and so the displacement will be zero. However, the distance may not be zero as the body may go from A to C and then from C back to B (which is the same as A in this case), where C is some other point. Then the length of the actual path taken by the body (the distance) is not zero.
Thus, displacement can be zero if the starting and ending points are the same, but distance can never be zero.
Hence the correct option is C) (c) only, i.e. displacement may or may not be equal to distance.

Note: Students might think that displacement is always smaller than distance in magnitude, but they should remember that the both can in fact, be equal, if the path taken by the body is a straight line between the starting and ending points.