All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
Class 12 Exam  >  Class 12 Questions  >  What will be the value of the co-ordinate who... Start Learning for Free
SaveJoin the Discussion on the App
What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?
  • a)
    (1, 1)
  • b)
    (2, 2)
  • c)
    (3, 3)
  • d)
    (4, 4)
Correct answer is option 'D'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Most Upvoted Answer
What will be the value of the co-ordinate whose position of a particle...
To find the coordinate of the particle, we need to determine the rates of increase of the abscissa (x-coordinate) and the ordinate (y-coordinate) along the parabola y^2 = 4x.

Let's differentiate the equation of the parabola with respect to x to find the rate of increase of y with respect to x.

Differentiating y^2 = 4x with respect to x using the chain rule, we get:
2yy' = 4
y' = 4/(2y)
y' = 2/y

Similarly, let's differentiate the equation of the parabola with respect to x to find the rate of increase of x with respect to y.

Differentiating y^2 = 4x with respect to y using the chain rule, we get:
2yy' = 4
y' = 4/(2y)
y' = 2/y

Since the rate of increase of the abscissa is twice the rate of increase of the ordinate, we have:
2/y = 2/(2/y)
2/y = y/2
4 = y^2
y = ±2

Now, substituting the value of y into the equation of the parabola, we can find the corresponding x-coordinate.

For y = 2:
y^2 = 4x
4 = 4x
x = 1

For y = -2:
y^2 = 4x
4 = 4x
x = 1

Therefore, the coordinate of the particle is (1, ±2).

Since the question asks for the coordinate where the rate of increase of the abscissa is twice the rate of increase of the ordinate, we consider the positive value of y, which is y = 2. Thus, the coordinate of the particle is (1, 2).

Hence, the correct answer is option D, (1, 2).
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
What will be the value of the co-ordinate whose position of a particle...
Here, y2 = 4x ….(1)
Let, (x, y) be the position of the particle moving along the parabola (1) at time t.
Now, differentiating both sides of (1) with respect to t, we get:
2y(dy/dt) = 4(dx/dt)
Or, y(dy/dt) = 2(dy/dt) ……….(2)
By question, dx/dt = 2 * dy/dt ……….(3)
From (2) and (3) we get, y(dy/dt) = 2 * 2 dy/dt
Or, y = 4
Putting y = 4 in (1) we get, 42 = 4x
So, x = 4
Thus, the co-ordinate of the particle is (4, 4).
< Previous Question Next Question >
Explore Courses for Class 12 exam

Similar Class 12 Doubts

A cyclotron is a kind of particle accelerator invented by Ernest O. Lawrence at the University of California, Berkeley, in 1929–1930, and patented in 1932. A cyclotron accelerates charged particles along a spiral path outward from the center. The particles are guided by a static magnetic field to a spiral trajectory, and accelerated by a rapidly changing electric field (radio frequency). For this invention Lawrence received the 1939 Nobel Prize in Physics.Cyclotrons were the most efficient particle accelerator equipment until the 1950s, when the synchrotron replaced them, and are now used in science and nuclear medicine to generate particle beams.This will toss the particle out of resonance with the oscillating field which means that when the particle reaches the hole between the dees, the extremity of the dees won't change. Thus, the particle won't be accelerated further.So, Cyclotron isn't reasonable for accelerating electrons. Because of the small mass, the speed of electrons increments quickly. Similarly, because of fast relativistic variation in their mass, the electrons escape step with the oscillating electric field.Hence, option A is the correct option.

What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer?
Question Description
What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer?.
Solutions for What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Here you can find the meaning of What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice What will be the value of the co-ordinate whose position of a particle moving along the parabola y2 = 4x at which the rate at of increase of the abscissa is twice the rate of increase of the ordinate?a)(1, 1)b)(2, 2)c)(3, 3)d)(4, 4)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 12 tests.
Explore Courses for Class 12 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup