Potential Energy Questions

An electric dipole with dipole moment $5\times 10^{-6}\text{Cm}$ is aligned with the direction of a uniform electric field of magnitude $4\times 10^5\text{N/C}$. The dipole is then rotated through an angle of $60^{\circ }$ with respect to the electric field. The change in the potential energy of the dipole is:

The potential energy of a system increases if work is done:

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is (q3/4πε 0)k, where k is :

Water falls from a height of $60\text{m}$ at the rate of $15\text{kg/s}$ to operate a turbine. The losses due to frictional forces are $10\%$ of the energy. How much power is generated by the turbine? (Take $g=10{\text{m/s}}^2$)

A block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

A bar magnet ($M=0.4{\text{JT}}^{-1}$) is in field $B=0.16\text{T}$. Potential energy in stable equilibrium is:

An electric dipole of moment $\vec{p}$ is placed in an electric field of intensity $\vec{E}$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta =90^{\circ }$, the torque and the potential energy of the dipole will respectively be:

The potential energy of a particle in a force field is $U=A/r^2-B/r$, where $A$ and $B$ are positive constants and $r$ is the distance of particle from the centre. For stable equilibrium the distance of the particle is:

A body of mass $m$ is taken from the earth's surface to the height equal to twice the radius ($R$) of the earth. The change in potential energy of the body will be: