$A$ rope is used to lower a block of mass $M$ vertically by a distance $x$ with a constant downward acceleration of $\frac{g}{2}$. The work done by the rope on the block is:

If $\overline{a}$ and $\overline{b}$ are two unit vectors such that $5 \overline{a} + 4 \overline{b}$ and $\overline{a} - 2 \overline{b}$ are perpendicular to each other,then the angle between $\overline{a}$ and $\overline{b}$ is

If a wire of length $L$ forms a loop of radius $R$ and has $n$ turns,find the magnetic field at the center of the loop. The current flowing in the loop is $I$.

$A$ convex lens $A$ of focal length $20 \ cm$ and a concave lens $B$ of focal length $5 \ cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam,then the distance $d$ in $cm$ will be

$A$ block can slide on a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with an acceleration $a$,the acceleration of the block relative to the incline is:

$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $R$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if