NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 3

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Question 4.7:

Given a + b + c + d = 0, which of the following statements are correct:

a) a, b, c, and d must each be a null vector.

b) The magnitude of (a + c) equals the magnitude of (b+ d).

c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.

d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?

Answer:

a) a, b, c, and d must each be a null vector : Incorrect.

Explanation: In order to make a + b + c + d = 0, it is not necessary to have all the four given vectors

to be null vectors. There are many other combinations, which can give the sum zero.

b) The magnitude of (a + c) equals the magnitude of (b + d) : Correct

Explanation: and,

Taking modulus on both the sides, we get:

Hence, the magnitude of (a + c) is the same as the magnitude of (b + d).

c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d : Correct

and

Taking modulus both sides, we get:

…( i )

Equation (i) shows that the magnitude of “a” is equal to or less than the sum of the magnitudes of b, c, and d.

Hence, the magnitude of vector a can never be greater than the sum of the magnitudes of

b, c, and d.

d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear : : Correct

Explanation:

For

The resultant sum of the three vectors a, (b + c), and d can be zero only if (b + c) lie in a plane containing a and d, assuming that these three vectors are represented by the three

Sides of a triangle.

If “a” and “d” are collinear, then it implies that the vector (b + c) is in the line of a and d. This implication holds only then the vector sum of all the vectors will be zero.

Question 4.8:

Three girls skating on a circular ice ground of radius 200 m start from a point P on the

edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Figure 4.8. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?

Find magnitude of the displacement vector by figure value.

Figure 4.8

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Fig. 4.8

Answer:

Displacement is given by the minimum distance between the initial and final positions of

a particle. In the given case, all the girls start from point P and reach point Q. The magnitudes of their displacements will be equal to the diameter of the ground.

Radius of the ground

Diameter of the ground

Hence, the magnitude of the displacement for each girl is 400 m. This is equal to the actual length of the path skated by girl B.