1. Tardigrade
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  4. A particle of mass 5kg moving in the x-y plane has its potential energy given by U=(.-7x+24y.)Joule , x and y being in meter . Initially at t=0 ,the particle is located at the origin (.0,0.) and moving with a velocity of 6[2.4 hati + 0.7 hatj]m/s . Find the magnitude of force acting on the particle.

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Q. A particle of mass $5kg$ moving in the $x-y$ plane has its potential energy given by $U=\left(\right.-7x+24y\left.\right)Joule$ , $x$ and $y$ being in $meter$ . Initially at $t=0$ ,the particle is located at the origin $\left(\right.0,0\left.\right)$ and moving with a velocity of $6\left[2.4 \hat{i} + 0.7 \hat{j}\right]m/s$ . Find the magnitude of force acting on the particle.

NTA AbhyasNTA Abhyas 2020

Solution:

$\overset{ \rightarrow }{F}= \, -\frac{\partial U}{\partial x} \, \hat{i}-\frac{\partial U}{\partial y} \, \hat{j}=7\hat{i}-24\hat{j} \, $
$\therefore $ $\left|\overset{ \rightarrow }{F}\right|= \, \sqrt{\left(7\right)^{2} + \left(- 24\right)^{2}}=25 \, unit$