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  • A particle of mass 2 kg moves on the x-axis under the influence of force of attraction acting towards the origin given by <img alt="\vec{F}=\frac{4}{x^{2}}i." src="https://entrancecorner.oncodecogs

A particle of mass 2 kg moves on the x-axis under the influence of force of attraction acting towards the origin given by \vec{F}=\frac{4}{x^{2}}i. If the particle starts from rest at x = 4 m, the speed it will attain to reach the point x = 2m will be
 

Option: 1

1\;m/s


Option: 2

2\;m/s


Option: 3

\frac{3}{2}\;m/s

 


Option: 4

\frac{1}{2}\;m/s


Answers (1)

best_answer

Answer (1)

F=\frac{-dU}{dx}

-dU=\frac{4}{x^{2}}dx

U_{f}-U_{i}=-\int_{4}^{2}4x^{-2}dx

U_{f}-U_{i}=4\left [ \frac{1}{x} \right ]_{4}^{2}

U_{f}-U_{i}=4\left [ \frac{1}{2} -\frac{1}{4}\right ]

\left ( U_{f}-U_{i} \right )=1

Posted by

rishi.raj

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