Question

If the displacement of a particle is equal to zero,

then its distance

(1) Must be equal to zero

(2) Can't be equal to zero

(3) Can be negative

(4) May or may not be equal to zero

Answer 1

If the displacement of a particle is equal to zero,

then its distance (4) May or may not be equal to zero.
______________________________

Displacement is the length of shortest path from initial point to Final point.
whereas distance is the length of path it took to go from Initial point to final point.

Example 1:
Let's say a boy is standing at one point. he is not moving. so displacement and distance, both are 0.

Example2:
If a boy starts from home, goes to market and returns home;
displacement is 0 as the initial and final point are the same.
but distance is not 0. he travelled the some distance to go from home to market and market to home.

We see that displacement is 0 in both cases, but distance is 0 in first case but not 0 in second case.

Answer 2

$\huge \red{hello}$

$\green{your \: answer \: is \: option \: (4)}$

$\huge{reason - - - }$

=> We know that the displacement is the shortest distance between the starting (u) and final positions (v) of a moving body in a particular distance.

=> Suppose if we walk some distance and then again come to the same point then what will be displacement simply then displacement will be zero because initial and final points are the same.

=> Let us we understand it by taking a numerical example.
Supposed you go school per day and the distance between school and your house is 10 km.You went School means initial point (u) is your home and once again came back means also the final point (v) is your home means the displacement is 0 but you walked 10 km (5km+5km).

$\huge \pink{so.......}$

We can say that If the displacement of a particle is equal to zero,then its distance
May or may not be equal to zero.

$\green{i \: hope \: it \: helped \: you}$

$\huge \red{thank \: you}$