(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

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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 force acting on a particle is given by the formula $F(x) = -kx + ax^3$. Find the graph of its potential energy $U(x)$ for $x \ge 0$.

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$A$ chain of mass $M$ and length $L$ is placed on a table such that $L/4$ of its length hangs over the edge. What is the work done by an external force to pull the hanging part back onto the table?

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The potential energy of a particle in a central field has the form $U(r) = \frac{1}{r^2} - \frac{1}{r}$, where '$r$' is the distance from the centre of the field. The magnitude of the maximum attractive force in Newton is

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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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$A$ uniform chain of length $2 \ m$ is placed on a table such that $60 \ cm$ of it hangs freely from the edge of the table. The total mass of the chain is $4 \ kg$. What is the work done in pulling the chain completely onto the table (in $J$)? (Take $g = 10 \ m/s^2$)

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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

The force acting on a particle is given by the formula $F(x) = -kx + ax^3$. Find the graph of its potential energy $U(x)$ for $x \ge 0$.

$A$ chain of mass $M$ and length $L$ is placed on a table such that $L/4$ of its length hangs over the edge. What is the work done by an external force to pull the hanging part back onto the table?

The potential energy of a particle in a central field has the form $U(r) = \frac{1}{r^2} - \frac{1}{r}$, where '$r$' is the distance from the centre of the field. The magnitude of the maximum attractive force in Newton is

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 ...........

$A$ uniform chain of length $2 \ m$ is placed on a table such that $60 \ cm$ of it hangs freely from the edge of the table. The total mass of the chain is $4 \ kg$. What is the work done in pulling the chain completely onto the table (in $J$)? (Take $g = 10 \ m/s^2$)

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