Motion in a Plane Test

Result

Motion in a Plane Test - 2

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Weekly Quiz Competition

Question 1
4 / -1

Which of the following is not a property of a null vector?

A

B
where λ is a scalar

C

D

Solution

Multiplying any vector by zero will result in a null vector.
So, the property of null vector is wrongly mention in option (C)
Hence, the correct option is (C).
Question 2
4 / -1

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

A
a, b, c, 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?

Solution

(a) Incorrect, because a + b + c + d can zero in many ways other than that (vector a, b, c, and d) must each be a null vector.
(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -(vector b + d).
Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.
(c) correct, Since (vector a + b + c + d = 0'
(vector a = -(b + c + d))
Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be greater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.
(d) Correct, because (vector a + b + c + d = 0;) hence ((vector b + c) + a + d = 0)
The resultant sum of three (vectors b + c, + a + d) can be zero only if (vector b + c) is in the plane of (vector a and d). In case vector a and d are collinear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.
Question 3
4 / -1

Two vectors A and B inclined at an angle θ have a resultant R which makes an angle α with A. If the directions of A and B are interchanged, the resultant will have the same

A
Direction

B
Magnitude

C
Direction as well as magnitude

D
None of these

Solution

Neither the magnitude of vectors nor the angle between the vectors is changed. So, magnitude of the resultant remains unchanged. However, the direction of the resultant will be changed.
Question 4
4 / -1

Three forces of magnitude 6 N, 6 N and √72 N act as a corner of a cube along three sides as shown in fig. Resultant of these forces is

A
12 N along OB

B
18 N along OA

C
18 N along OC

D
12 N along OE

Solution

Let sides OC, OG and OA represent x, y and z respectively.
Resultant of forces = 6i + √72 j + 6j = vector R
R = √(36 + 72 + 36) = √144 = 12 N
Resultant of OA and OC is along OB and of magnitude √72
(∵ they are perpendicular)
∴ Resultant of OC, OG and OA is same as OB √72 + OG √72
Its resultant will be along OE.
Question 5
4 / -1

Rain is falling vertically with a speed of 35ms⁻¹. Winds starts blowing after sometime with a speed of 12ms⁻¹ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

A

B

C

D

Solution

The velocity of the rain and the wind are represented by the vectors as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity If θ is the angle which resultant velocity makes with the vertical, then