NEET Exam  >  NEET Questions  >  If the linear density (mass per unit length) ... Start Learning for Free
If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]
  • a)
    2.5 m
  • b)
    1 m
  • c)
    1.5 m
  • d)
    2 m
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the linear density (mass per unit length) of a rod of length 3m is ...
Given, linear density of the rod is proportional to x, where x is the distance from one end of the rod.

Let the linear density of the rod at distance x from one end be ρ(x).

We know that the mass of an element of length dx at a distance x from one end is given by dm = ρ(x) dx.

The total mass of the rod is given by integrating the above expression from 0 to 3m:

M = ∫₀³ ρ(x) dx

We also know that the position of the centre of gravity of the rod is given by:

x_bar = (1/M) ∫₀³ x ρ(x) dx

Substituting dm = ρ(x) dx in the above expression, we get:

x_bar = (1/M) ∫₀³ x dm

x_bar = (1/M) ∫₀³ x ρ(x) dx

x_bar = (1/M) ∫₀³ x (kx) dx (since ρ(x) is proportional to x)

x_bar = (k/M) ∫₀³ x² dx

x_bar = (k/M) [x³/3]₀³

x_bar = (k/M) [3³/3]

x_bar = 3k/M

But we know that M = ∫₀³ ρ(x) dx

M = k ∫₀³ x dx

M = k [x²/2]₀³

M = k (9/2)

Therefore, x_bar = 3k/M = 3k/(k(9/2)) = 2/3 * 3 = 2m

Hence, the distance of the centre of gravity of the rod from one end is 2m, which is option D.
Free Test
Community Answer
If the linear density (mass per unit length) of a rod of length 3m is ...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
Explore Courses for NEET exam

Top Courses for NEET

If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer?
Question Description
If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer?.
Solutions for If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET. Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is[2002]a)2.5 mb)1 mc)1.5 md)2 mCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
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