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Test: Motion in a Plane (May 21) - JEE MCQ


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15 Questions MCQ Test - Test: Motion in a Plane (May 21)

Test: Motion in a Plane (May 21) for JEE 2024 is part of JEE preparation. The Test: Motion in a Plane (May 21) questions and answers have been prepared according to the JEE exam syllabus.The Test: Motion in a Plane (May 21) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Motion in a Plane (May 21) below.
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*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 1

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure.
A vertical force  of magnitude 100 N is applied at point A of the frame.



Suppose the force is  resolved parallel to the arms AB and AC of the frame. The magnitude of the resolved component along the arm AC is xN. The value of x, to the nearest integer, is _________.
[Given: sin (35°) = 0.573, cos (35°) = 0.819 sin (110°) = 0.939, cos (110°) = -0.342]


Detailed Solution for Test: Motion in a Plane (May 21) - Question 1



Component along AC
= 100 cos 35°N
= 100 × 0.819 N
= 81.9 N
≈ 82 N

Test: Motion in a Plane (May 21) - Question 2

A player kicks a football with an initial speed of 25 ms-1 at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach the highest point during motion? (Take g = 10 ms-2)

Detailed Solution for Test: Motion in a Plane (May 21) - Question 2


= 15.625 m

= 2.5 × 0.7
= 1.77 s

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Test: Motion in a Plane (May 21) - Question 3

A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become:

Detailed Solution for Test: Motion in a Plane (May 21) - Question 3



E = 1/2mu2
At highest point, velocity V = u cos60° = u/2
 K.E. at topmost point = 

Test: Motion in a Plane (May 21) - Question 4

A ball is projected from the ground with a speed 15 ms-1 at an angle θ with horizontal so that its range and maximum height are equal, then tan θ will be equal to

Detailed Solution for Test: Motion in a Plane (May 21) - Question 4

Given: R = H

 u cos 
tanθ = 4

*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 5

A ball is projected vertically upward with an initial velocity of 50 ms-1 at t = 0 s. At t = 2 s, another ball is projected vertically upward with same velocity. At t = _______ s, second ball will meet the first ball (g = 10 ms-2). (in integers)


Detailed Solution for Test: Motion in a Plane (May 21) - Question 5

*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 6

A swimmer can swim with velocity 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is __________ (in degrees).
(Round off to the nearest integer)


Detailed Solution for Test: Motion in a Plane (May 21) - Question 6



vm = 12 km/h
vr = 6 km/h
vm sin θ = vr
sin θ = 
θ = 30°
α = 90 + θ
α = 90 + 30
α = 120°

*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 7

A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is ______.


Detailed Solution for Test: Motion in a Plane (May 21) - Question 7



x = 10 sin 30°



x = 5 m/s

*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 8

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ with the line AB should be _____ °, so that the swimmer reaches point B. (in integers)


Detailed Solution for Test: Motion in a Plane (May 21) - Question 8



Both velocity vectors are of same magnitude, so the resultant would pass exactly midway through them.
θ = 30°

Test: Motion in a Plane (May 21) - Question 9

At time t = 0, a particle starts travelling from a height 7 cm in a plane keeping z coordinate constant. At any instant of time, its position along the  and  directions is defined as 3t and 5t3, respectively. At t = 1 s, acceleration of the particle will be

Detailed Solution for Test: Motion in a Plane (May 21) - Question 9

Test: Motion in a Plane (May 21) - Question 10

The resultant of these force  and  is approximately ___________ N.
[Take  = 1.7,  = 1.4 Given  and  unit vector along x, y axis]

Detailed Solution for Test: Motion in a Plane (May 21) - Question 10

Test: Motion in a Plane (May 21) - Question 11

Two vectors  and  have equal magnitudes. If magnitude of  is equal to two times the magnitude of , then the angle between  and  will be:

Detailed Solution for Test: Motion in a Plane (May 21) - Question 11

(a2 + b2 + 2ab cos) = 4(a2 + b2 - 2ab cosθ)
Put a = b.
2a2 + 2a2 cosθ = 8a2 - 8a2 cosθ
cosθ = 
θ = 

*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 12

A body of mass 2 kg moves under a force of N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is ________. (Round off to the nearest integer)


Detailed Solution for Test: Motion in a Plane (May 21) - Question 12






b = 12

Test: Motion in a Plane (May 21) - Question 13

Statement I: Two forces  and  where , when act at an angle  to each other, the magnitude of their resultant is , when they act at an angle , the magnitude of their resultant becomes  . This is possible only when .

Statement II: In the situation given above.
 = 60° and  = 90°

In the light of the above statements, choose the most appropriate answer from the options given below

Detailed Solution for Test: Motion in a Plane (May 21) - Question 13


 


For 

For 

Test: Motion in a Plane (May 21) - Question 14

A particle of mass m is projected with a speed u from the ground at an angle θ = π / 3 w.r.t. horizontal axis (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity u. The horizontal distance covered by the combined mass before reaching the ground is:

Detailed Solution for Test: Motion in a Plane (May 21) - Question 14

2mvx = mu + mu cos 60°
Vx = 3u / 4



Horizontal range after collision:

*Answer can only contain numeric values
Test: Motion in a Plane (May 21) - Question 15

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ____ s.(In Integers)


Detailed Solution for Test: Motion in a Plane (May 21) - Question 15

Based on the situation,

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