Motion in a Plane Test

Result

Motion in a Plane Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Two balls are projected simultaneously with the same speed from the top of a tower, one vertically upwards and the other vertically downwards. They reach the ground in 9 s and 4 s, respectively. What is the height of the tower?
(g = 10 m/s²)

A
180 m

B
300 m

C
350 m

D
400 m
Question 2
1 / -0

The motion of the wheel of a cycle is

A
rectilinear

B
rotatory

C
translatory

D
translatory and rotatory
Question 3
1 / -0

It is found that (range)² is 48 times the (maximum height)² for a trajectory. Find the angle of projection.

A
60^o

B
30^o

C
45^o

D
75^o
Question 4
1 / -0

The displacement x of a particle varies with time t as , where a, b, α and β are positive constants. The velocity of the particle will

A
go on decreasing with time

B
be independent of α and β

C
drop to zero when α = β

D
go on increasing with time
Question 5
1 / -0

An arbitrary vector v can be expressed as

A
a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to 1

B
a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to -1

C
a sum of three mutually perpendicular unit vectors each multiplied by a some scalar constant

D
a sum of three mutually perpendicular unit vectors each multiplied by the same scalar constant

Solution

Set of elements (vectors) in a vector space is called a basis, or a set of basis vectors, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.In more general terms, a basis is a linearly independent spanning set.

Given a basis of a vector space, every element of vector space can be expressed uniquely as a linear combination of basis vectors, whose coefficients are referred to as vector coordinates or components.

We can represent vector v as
Question 6
1 / -0

Directions: The following question has four choices out of which ONLY ONE is correct.

What type of path is followed by a projectile?

A
Elliptical

B
Parabolic

C
Hyperbolic

D
None of these
Question 7
1 / -0

We can define the difference of two vectors A and B as the

A
sum of two vectors A and B' such that B' is equal to B multiplied by 0

B
sum of two vectors A and B' such that B' is equal to B multiplied by -2

C
sum of two vectors A and B' such that B' is equal to B multiplied by -1

D
sum of two vectors A and B' such that B' is equal to B multiplied by 1
Solution
Explanation:Vector subtraction is defined in the following way.
- The difference of two vectors, A - B , is a vector C that is, C = A - B
- The addition of two vector such that C = A + (-B). B has been taken in opposite direction.
Thus vector subtraction can be represented as a vector addition.
Question 8
1 / -0

The friction of air causes a vertical retardation equal to the 10% of the acceleration due to gravity. The maximum height will be decreased by (take g = 10 ms^-2)

A
8%

B
9%

C
10%

D
11%
Question 9
1 / -0

A bomber plane is moving horizontally with a speed of 500 m/s and a bomb released from it strikes the ground in 10 seconds. The angle with the horizontal at which the bomb strikes the ground is (g = 10 m/s²)

A
tan^-1(1)

B
tan^-1(5)

C

D
Question 10
1 / -0

If and , then the angle made by ( + )with x-axis is

A
30^o

B
45^o

C
60^o

D
90^o
Question 11
1 / -0

If a ball is thrown vertically upwards with speed 'u', then the distance covered during the last 't' seconds of its ascent is

A

B
(u + gt)t

C
ut

D
Question 12
1 / -0

The angle of projection θ for which the horizontal range is equal to the maximum height attained by a projectile is

A
tan^-1 4

B
tan^-1 5

C
tan^-1 4/5

D
tan^-1 5/4
Question 13
1 / -0

Directions: The following question has four choices out of which ONLY ONE is correct.

Force of 100 N makes an angle of 30° with the horizontal. The vertical component of the force will be

A
100 sin 30°

B
100 cos 30°

C
100 sin 60°

D
100 sin 90°
Question 14
1 / -0

A

B

C

D

Solution

In a two-dimensional coordinate system, any vector can be broken into x -component and y -component.
Question 15
1 / -0

A

B

C

D

Solution

Rectangular component of a Vector: The projections of vector a along the x, y, and z directions are Ax, Ay, and Az, respectively.
Question 16
1 / -0

Directions: The following question has four choices out of which ONLY ONE is correct.

For the angles of projection of a projectile as (45^o - θ) and (45^o + θ), the horizontal ranges described by the projectile are in the ratio

A
1 : 1

B
2 : 3

C
1 : 2

D
2 : 1
Question 17
1 / -0

Directions: The following question has four choices, out of which ONLY ONE is correct.

A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the time periods of the flights in two cases, what is the product of the two time periods of the flights proportional to?

A

B

C

D
Question 18
1 / -0

If and are non-zero vectors which obey the relation , then the angle between them is

A
0°

B
60°

C
90°

D
120°
Question 19
1 / -0

If a particle is projected with a velocity 'u' so that its horizontal range is twice the greatest height attained, then what is the horizontal range?

A

B

C

D
None of these
Question 20
1 / -0

A unit vector is a vector

A
having a magnitude of 1 and points in y-direction

B
having a magnitude of 1 and points in x-direction

C
having a magnitude of 1 and points in z-direction

D
having a magnitude of 1 and points in any chosen direction

Solution

A unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat": (pronounced "i-hat"). The term direction vector is used to describe a unit vector being used to represent spatial direction.