The circumference of a circle is measured as $56 \text{ cm}$ with an error of $0.02 \text{ cm}$. The percentage error in its area is

$A$ parallel plate capacitor of capacity $100 \mu F$ is charged by a battery of $50 \text{ V}$. The battery remains connected,and if the plates of the capacitor are separated so that the distance between them becomes double the original distance,the additional energy supplied by the battery to the capacitor in joules is:

Two tangent galvanometers $A$ and $B$ have coils of radii $8 \, cm$ and $16 \, cm$ respectively and resistance $8 \, \Omega$ each. They are connected in parallel with a cell of emf $4 \, V$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30°$ and $60°$ respectively. If $A$ has $2$ turns, then $B$ must have: (in $turns$)

The magnetic needle of a vibration magnetometer makes $12$ oscillations per minute in the horizontal component of the earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line,it makes $15$ oscillations per minute. If the poles of the bar magnet are interchanged,the number of oscillations it makes per minute is

The binding energy of deuteron ${}_1^2H$ is $1.112 \, MeV$ per nucleon and an $\alpha$-particle ${}_2^4He$ has a binding energy of $7.047 \, MeV$ per nucleon. Then in the fusion reaction ${}_1^2H + {}_1^2H \to {}_2^4He + Q$,the energy $Q$ released is ......... $MeV$.

Calcium hydride on hydrolysis forms