SATHEE: Rotational Motion Question 106

Rotational Motion Question 106

Question: The centre of mass of a non-uniform rod of length $L$ whose mass per unit length $λ$ varies as $λ = \frac{k . x^{2}}{L}$ where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)

Options:

A) $\frac{3}{4} L$

B) $\frac{1}{4} L$

C) $\frac{k}{L}$

D) $\frac{3 k}{L}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a]

$∴ x_{c m} \frac{\int_{0}^{L} \frac{K}{L} x^{2} d x \cdot x}{\int_{0}^{L} \frac{K}{L} x^{2} d x} = \frac{{\frac{x^{4}}{4} |}_{0}^{L}}{{\frac{x^{3}}{3} |}_{0}^{L}} = \frac{3}{4} L$

Rotational Motion Question 106

Question: The centre of mass of a non-uniform rod of length $L$ whose mass per unit length $λ$ varies as $λ = \frac{k . x^{2}}{L}$ where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)

Options:

Answer:

Solution:

Engineering Preparation

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NCERT Books & Solutions

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Other Resources

Syllabus

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Mentorship

NCERT Exercise Video Solution

Rotational Motion Question 106

Question: The centre of mass of a non-uniform rod of length L whose mass per unit length λ varies as λ=k.x2L where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The centre of mass of a non-uniform rod of length $L$ whose mass per unit length $λ$ varies as $λ = \frac{k . x^{2}}{L}$ where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)