Important questions based on NCERT syllabus for Chapter 4 - Motion in a Plane:
Question-1: Can you associate vectors with (a) the length of a wire bent into a loop (b) a plane area (c) a sphere? Explain.
Solution: (a) We cannot associate a vector with the length of a wire bent into a loop. This is because the length of the loop does not have a definite direction.
(b) We can associate a vector with a plane area. Such a vector is called area vector and its direction is represented by a normal drawn outward to the area.
(c) The area of a sphere does not point in any difinite direction. However, we can associate a null vector with the area of the sphere. We cannot associate a vector with the volume of a sphere.
Question-2: From the following pick any two scalar quantities:
Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic momentum, relative velocity.
Dot product of force and displacement is the work done. Work is a scalar quantity since dot product of two quantity is always scalar.
Current is a scalar quantity as it is described only by its magnitude and it is independent of direction.
Question-3: Does a vector have a location in space? Will it fluctuate with time? Can two equivalent vectors x and y at various locations in space fundamentally have indistinguishable physical effects? Give cases in support of your answer.
Solution: No, Yes and No.
A vector in space has no distinct location. The reason behind this is that a vector stays invariant when it displaces in a way that its direction and magnitude does not change. Although, a position vector has a distinct location in space.
A vector change with time. For instance, the velocity vector of a ball moving with a specific speed fluctuates with time.
Two equivalent vectors situated at different locations in space do not generate the same physical effect. For instance, two equivalent forces acting at different points on a body tend to rotate the body, but the combination will not generate the equivalent turning effect.