(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, Power and Collision Potential Energy

Medium

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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Work, Energy, Power and Collision

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Potential Energy

$A$ chain of length $L$ and mass $M$ is placed on a frictionless table with one-fifth of its length hanging over the edge. What is the work required to pull the hanging part back onto the table?

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The potential energy between two atoms is given by the function $U(r) = a/r^{12} - b/r^{6}$. Find the equilibrium distance between them.

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$A$ smooth chain of length $2 \,m$ is kept on a table such that its length of $60 \,cm$ hangs freely from the edge of the table. The total mass of the chain is $4 \,kg$. The work done in pulling the entire chain on the table is (Take, $g=10 \,m/s^2$) (in $\,J$)

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$A$ chain of mass $M$ and length $L$ is placed on a smooth table such that $1/n$ of its length is hanging over the edge of the table. The hanging part of the chain is pulled back onto the surface of the table. Find the work done to pull it up.

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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 ................ $J$.

Similar Questions

$A$ chain of length $L$ and mass $M$ is placed on a frictionless table with one-fifth of its length hanging over the edge. What is the work required to pull the hanging part back onto the table?

$A$ particle is released from rest at the point $x = a$ and moves along the $x$ axis subject to the potential energy function $U(x)$ shown. The particle:

The potential energy between two atoms is given by the function $U(r) = a/r^{12} - b/r^{6}$. Find the equilibrium distance between them.

$A$ smooth chain of length $2 \,m$ is kept on a table such that its length of $60 \,cm$ hangs freely from the edge of the table. The total mass of the chain is $4 \,kg$. The work done in pulling the entire chain on the table is (Take, $g=10 \,m/s^2$) (in $\,J$)

$A$ chain of mass $M$ and length $L$ is placed on a smooth table such that $1/n$ of its length is hanging over the edge of the table. The hanging part of the chain is pulled back onto the surface of the table. Find the work done to pull it up.

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