355572 The potential energy of a 1 \(kg\) particle free to move along the \(x\)-axis is given by \(V(x)=\left(\dfrac{x^{4}}{4}-\dfrac{x^{2}}{2}\right) J\). The total mechanical energy of the particle is 2\(J\). Then, the maximum speed (in \(m/s\)) is

355573 The potential energy function (in \(J\) ) of a particle in a region of space is given as\(U=\left(2 x^{2}+3 y^{3}+2 z\right)\). Here \(x, y\) and \(z\) are in meter. The magnitude of \(x\)-component of force (in \(N\) ) acting on the particle at point \(P(1,2,3) m\) is

355574 The potential energy \(U\) in joule of a particle of mass 1 \(kg\) moving in \(x-y\) plane obeys the law \(U=3 x+4 y\), where \((x, y)\) are the co-ordinates of the particle in metre. If the particle is at rest at \((6,4)\) at time \(t=0\) then identify the wrong statement:

355575 The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \(U(x)=\dfrac{a}{x^{12}}-\dfrac{b}{x^{6}}\), where \(a\) and \(b\) are constants and \(x\) is the distance between the atoms. The dissociation energy of the molecule is \(D = \left[ {U(x = \infty ) - {U_{{\rm{at}}\,\,{\rm{equilibrium }}}}} \right],D\) is

355572 The potential energy of a 1 \(kg\) particle free to move along the \(x\)-axis is given by \(V(x)=\left(\dfrac{x^{4}}{4}-\dfrac{x^{2}}{2}\right) J\). The total mechanical energy of the particle is 2\(J\). Then, the maximum speed (in \(m/s\)) is

355573 The potential energy function (in \(J\) ) of a particle in a region of space is given as\(U=\left(2 x^{2}+3 y^{3}+2 z\right)\). Here \(x, y\) and \(z\) are in meter. The magnitude of \(x\)-component of force (in \(N\) ) acting on the particle at point \(P(1,2,3) m\) is

355574 The potential energy \(U\) in joule of a particle of mass 1 \(kg\) moving in \(x-y\) plane obeys the law \(U=3 x+4 y\), where \((x, y)\) are the co-ordinates of the particle in metre. If the particle is at rest at \((6,4)\) at time \(t=0\) then identify the wrong statement:

355575 The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \(U(x)=\dfrac{a}{x^{12}}-\dfrac{b}{x^{6}}\), where \(a\) and \(b\) are constants and \(x\) is the distance between the atoms. The dissociation energy of the molecule is \(D = \left[ {U(x = \infty ) - {U_{{\rm{at}}\,\,{\rm{equilibrium }}}}} \right],D\) is

355572 The potential energy of a 1 \(kg\) particle free to move along the \(x\)-axis is given by \(V(x)=\left(\dfrac{x^{4}}{4}-\dfrac{x^{2}}{2}\right) J\). The total mechanical energy of the particle is 2\(J\). Then, the maximum speed (in \(m/s\)) is

355573 The potential energy function (in \(J\) ) of a particle in a region of space is given as\(U=\left(2 x^{2}+3 y^{3}+2 z\right)\). Here \(x, y\) and \(z\) are in meter. The magnitude of \(x\)-component of force (in \(N\) ) acting on the particle at point \(P(1,2,3) m\) is

355574 The potential energy \(U\) in joule of a particle of mass 1 \(kg\) moving in \(x-y\) plane obeys the law \(U=3 x+4 y\), where \((x, y)\) are the co-ordinates of the particle in metre. If the particle is at rest at \((6,4)\) at time \(t=0\) then identify the wrong statement:

355575 The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \(U(x)=\dfrac{a}{x^{12}}-\dfrac{b}{x^{6}}\), where \(a\) and \(b\) are constants and \(x\) is the distance between the atoms. The dissociation energy of the molecule is \(D = \left[ {U(x = \infty ) - {U_{{\rm{at}}\,\,{\rm{equilibrium }}}}} \right],D\) is

355572 The potential energy of a 1 \(kg\) particle free to move along the \(x\)-axis is given by \(V(x)=\left(\dfrac{x^{4}}{4}-\dfrac{x^{2}}{2}\right) J\). The total mechanical energy of the particle is 2\(J\). Then, the maximum speed (in \(m/s\)) is

355573 The potential energy function (in \(J\) ) of a particle in a region of space is given as\(U=\left(2 x^{2}+3 y^{3}+2 z\right)\). Here \(x, y\) and \(z\) are in meter. The magnitude of \(x\)-component of force (in \(N\) ) acting on the particle at point \(P(1,2,3) m\) is

355574 The potential energy \(U\) in joule of a particle of mass 1 \(kg\) moving in \(x-y\) plane obeys the law \(U=3 x+4 y\), where \((x, y)\) are the co-ordinates of the particle in metre. If the particle is at rest at \((6,4)\) at time \(t=0\) then identify the wrong statement:

355575 The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \(U(x)=\dfrac{a}{x^{12}}-\dfrac{b}{x^{6}}\), where \(a\) and \(b\) are constants and \(x\) is the distance between the atoms. The dissociation energy of the molecule is \(D = \left[ {U(x = \infty ) - {U_{{\rm{at}}\,\,{\rm{equilibrium }}}}} \right],D\) is