The total mechanical enegry of a particle is `E`. The speed of the particle at `x = ((2E)/(K))^(1//2)` is `((2E)/(m))^(1//2)`. Find the potential energy of the particle at `x` :

The total mechanical energy of a particle of mass m executing SHM with the help of a spring is E = (1//2)momega^(2)A^(2) . If the particle is replaced by another particle of mass m//2 while the amplitude A remains same. New mechanical energy will be :

The potential energy of a 2 kg particle free to move along the x- axis is given by V(x)[(x^(4))/(4)-(x^(2))/(2)]jou l e The total mechanical energy of the particle is 0.75 J . The maximum speed of the particle ( in m//s) is :

The potential energy of a 1kg particle free to move along the x-axis is given by V(x)=(x^(4)/4-x^(2)/2)J The total mechanical energy of the particle is 2J then the maximum speed (in m//s) is

The potential energy of a particle of mass 1 kg free to move along x-axis is given by U(x) =(x^(2)/2-x) joule. If total mechanical energy of the particle is 2J then find the maximum speed of the particle. (Assuming only conservative force acts on particle)

The potential energy of a particle of mass m is given by U=(1)/(2)kx^(2) for x lt 0 and U = 0 for x ge 0 . If total mechanical energy of the particle is E. Then its speed at x = sqrt((2E)/(k)) is

The potential energy of a particle of mass m is given by U=(1)/(2)kx^(2) for x lt 0 and U = 0 for x ge 0 . If total mechanical energy of the particle is E. Then its speed at x = sqrt((2E)/(k)) is