Question

Statement 1: If the initial and final position coincides, the displacement is a null vector because
Statement 2: A physical quantity cannot be called a vector if its magnitude is zero.
(A) Statement 1 is true, statement 2 is true. Statement 2 is the correct explanation of statement 1
(B) Statement 1 is true, statement 2 is true. Statement 2 is not the correct explanation of statement 1
(C) Statement 1 is true and statement 2 is false.
(D) Statement 1 is false and statement 2 is true.

Answer 1

Hint: Displacement is a vector quantity and to determine a vector quantity graphically we need to have initial and final position and from that, we can determine the magnitude and direction of that vector. A vector has both magnitude and direction, unlike scalars which have only magnitude.

Complete step by step answer:
Given that both the initial and final positions coincide so the magnitude of the vector is zero. Also, the displacement is the shortest distance between the initial and final position, hence the given displacement vector is zero in magnitude. Also, the zero vector or null vector is the vector whose magnitude is zero. So, the first statement is true.
Now, the second statement states that a physical quantity cannot be called a vector if its magnitude is zero but by the definition of null vector or zero vector this statement does not hold. Hence, the second statement is not true. So, the correct option is (C).

Note:Most of the time we get confused that if the magnitude is zero then the given quantity cannot be termed as a vector but in actual it depends upon the state of the quantity. If the distance between two points is zero then that cannot be called a zero vector because distance is not a vector quantity but that holds true for displacement.