Motion in a Plane Test

Result

Motion in a Plane Test - 5

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Weekly Quiz Competition

Question 1
4 / -1

The (x, y, z) coordinates of two points A and B are given respectively as (0, 4, -2) and (-2, 8, -4). The displacement vector from A to B is:

A

B

C

D

Solution

Displacement vector from A to B is given by
Question 2
4 / -1

A person moves 30 m north, then 30 m east, then 30√2 m south-west. His displacement from the original position is:

A
zero

B
28 m towards south

C
10 m towards west

D
15 m towards east

Solution

Resolving displacement 30√2 m south-west into two rectangular components, we get
Displacement in south

∴ Effective displacement due to 30 m north and 30 m south is zero.
Also effective displacement due to 30 m east and 30 m west in zero.
Question 3
4 / -1

A bird flies from (-3m, 4m, -3m) to (7m, -2m, -3m) in the xyz- coordinates. The bird's displacement vector is given by

A

B

C

D

Solution
Question 4
4 / -1

On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, the displacement of the motorist at the third turn is

A
500 m

B
500√3 m

C
1000 m

D
1000√3 m

Solution

The path followed by the motorist is a regular hexagon ABCDEF of side 500 m, as shown in the given figure. Let the motorist starts from A and takes the third turn at D.

Therefore, the magnitude of this displacement is
AD = AG + GD = 500 m + 500 m = 1000 m
Question 5
4 / -1

Four girls skating on 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. For which girl displacement is equal to the actual length of path?

A
A

B
B

C
C

D
D

Solution

Displacement of each girl =
Magnitude of displacement for each girl
For girl C, displacement = actual length of path.
Question 6
4 / -1

A particle starts moving from point (2, 10, 1). Displacement for the particle is The final coordinates of the particle is

A
(10, 8, 2)

B
(8, 10, 2)

C
(2, 10, 8)

D
(8, 2, 10)

Solution

Initial position vector of the particle,
Let final position vector of the particle be

Hence, the final coordinates of the particle are ((10, 8, 2)
Question 7
4 / -1

For any arbitrary motion in space, which of the following relations is true?

A

B

C

D

Solution

The relation (b) is true, others are false because relations (a), (c) and (d) hold only for uniformly accelerated motion.
Question 8
4 / -1

The position of a particle is given by where t is in seconds and the coefficients have the proper units forto be in metres. The direction of velocity of the particle at t = 1 s is

A
53^o with x-axis

B
37^o with x-axis

C
30^o with y-axis

D
60^o with y-axis

Solution

Let θ be angle which the direction ofmakes with the
Question 9
4 / -1

The acceleration of the particle at t = 1 is

A

B

C

D

Solution

From the previous question,

Acceleration of the particle remains constant at all times.
Question 10
4 / -1

If x = 5t + 3t² andy = 4t are the x and y co-ordinates of a particle at any time t second where x and y are in metre, then the acceleration of the particle

A
is zero throughout its motion

B
is a constant throughout its motion

C
depends only on its y component

D
varies along both x and y direction