(C) The potential energy function is $U(x) = 20 + (x - 2)^2$.The minimum potential energy $(U_{min})$ occurs when $(x - 2)^2 = 0$,which is at $x = 2\,

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(C) The potential energy function is $U(x) = 20 + (x - 2)^2$.The minimum potential energy $(U_{min})$ occurs when $(x - 2)^2 = 0$,which is at $x = 2\,m$.Thus,$U_{min} = 20 + 0 = 20\,J$.The total mechanical energy $(TE)$ of the particle is given as $36\,J$.According to the law of conservation of mechanical energy,$TE = U + KE$.To find the maximum kinetic energy $(KE_{max})$,we use the relation $KE_{max} = TE - U_{min}$.Substituting the values,$KE_{max} = 36\,J - 20\,J = 16\,J$.

Class 11 Physics Work, Energy and Power Potential Energy

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The potential energy of a particle oscillating along the $x-$axis is given by $U = 20 + (x - 2)^2$,where $U$ is in joules and $x$ is in meters. The total mechanical energy of the particle is $36\,J$. The maximum kinetic energy of the particle is ................ $J$.

A
$24$
B
$36$
C
$16$
D
$20$

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The $PE$ of a $2 \, kg$ particle,free to move along the $x$-axis,is given by $V(x) = \left( \frac{x^3}{3} - \frac{x^2}{2} \right) \, J$. The total mechanical energy of the particle is $4 \, J$. The maximum speed (in $m \, s^{-1}$) is ...........

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The potential energy of a particle oscillating along the $x-$axis is given by $U = 20 + (x - 2)^2$,where $U$ is in joules and $x$ is in meters. The total mechanical energy of the particle is $36\,J$. The maximum kinetic energy of the particle is ................ $J$.

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$A$ particle with constant total energy $E$ moves in one dimension in a region where the potential energy is $U(x)$. The speed of the particle is zero where

If the potential energy of a particle is given by $U = A - Bx^2$,then the force is proportional to which of the following?

$A$ rod of mass $m$ and length $l$ is lying on a table. What is the work done to make it stand vertically?

Potential energy as a function of $r$ is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$,where $r$ is the interatomic distance,and $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be

The $PE$ of a $2 \, kg$ particle,free to move along the $x$-axis,is given by $V(x) = \left( \frac{x^3}{3} - \frac{x^2}{2} \right) \, J$. The total mechanical energy of the particle is $4 \, J$. The maximum speed (in $m \, s^{-1}$) is ...........

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