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Physics - W.E.P. Question with Solution | TestHub

PhysicsW.E.P.MiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

A block of mass $2 kg$ is kept at origin at $t = 0$ and is having velocity $4 \sqrt{5} m / s$ in positive $x -$ direction. The only force on it is a conservative and its potential energy is defined as $U = - x^{3} + 6 x^{2} + 15$ ( $SI$ units). Its velocity when the force acting on it is minimum (after the time $t = 0$ ) is

Options:

Answer:

Solution:

At $x = 0$

$K = \frac{1}{2} \times 2 \times 80 = 80 J$ and $U = 15 J$

$∴$ Total energy is,

$E = K + U = 95 J$

Force, $F = \frac{- dU}{dx}$

$\Rightarrow F = 3 x^{2} - 12 x$

For $F$ to be minimum, $\frac{dF}{dx} = 0$

$\Rightarrow x = 2 m$

At $x = 2 m$

$E = K + U$

$\Rightarrow 95 = \frac{1}{2} \times 2 \times v^{2} + (- 8 + 24 + 15)$

$\Rightarrow v = 8 m / s$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:W.E.P.Subtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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