SATHEE: Work Power and Energy 5 Question 10

Work Power and Energy 5 Question 10

13. A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $X$ -axis. Its kinetic energy $K$ changes with time as $d K / d t = γ t$ , where $Y$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

(2018 Adv.)

(a) The force applied on the particle is constant

(b) The speed of the particle is proportional to time

(d) The force is conservative

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Answer:

Correct Answer: 13. (a, b)

Solution:

$(a, b)$ $K = \frac{1}{2} m v^{2}$

$\Rightarrow \frac{d K}{d t} = m v \frac{d v}{d t}$

Given, $\frac{d K}{d t} = γ t$

$\Rightarrow m v \frac{d v}{d t} = γ t$

$\Rightarrow \int_{0}^{v} v d v = \int_{0}^{t} \frac{Y}{m} t d t$

$\Rightarrow \frac{v^{2}}{2} = \frac{Y}{m} \frac{t^{2}}{2}$

$\Rightarrow v = \sqrt{\frac{Y}{m}} t$

$\Rightarrow a = \frac{d v}{d t} = \sqrt{\frac{Y}{m}}$

$∴ F = m a = \sqrt{Y m} =$ constant

$∴ V = \frac{d s}{d t} = \sqrt{\frac{Y}{m}} t \Rightarrow s = \sqrt{\frac{Y}{m}} \frac{t^{2}}{2}$

NOTE

Force is constant. In the website of IIT, option (d) is given correct. In the opinion of author all constant forces are not necessarily conservative. For example : viscous force at terminal velocity is a constant force but it is not conservative.

Work Power and Energy 5 Question 10

Answer:

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Work Power and Energy 5 Question 10

13. A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the X-axis. Its kinetic energy K changes with time as dK/dt=γt, where Y is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Answer:

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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