A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x(t) = \alpha t^2 + \beta t + \gamma$ m, where $\alpha = 1 \; m/s^2$, $\beta = 1 \; m/s$ and $\gamma = 1 \; m$. The work done on the body during the time interval $t = 2 \; s$ to $t = 3 \; s$, is ________ J.

A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when:

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is:

(Take $k = \frac{1}{4 \pi \epsilon_0}$ and assume $kQ^2 > Gm^2$ where $G$ is the Gravitational constant)

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is ________ s.