$A$ satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in the figure. The ratio of the speed of the satellite at point $a$ to that at point $b$ is

$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet,the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

$A$ coil of self-inductance $L$ is connected in series with a bulb $B$ and an $A.C.$ source. Brightness of the bulb decreases when

The plates of a parallel plate capacitor are charged up to $100 \, V$. $A$ $2 \, mm$ thick dielectric plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6 \, mm$. The dielectric constant of the plate is:

The area of the triangle $ABC$ is $10 \sqrt{3} \text{ cm}^2$,angle $B$ is $60^{\circ}$ and its perimeter is $20 \text{ cm}$,then $\ell(AC) = $ (in $\text{ cm}$)

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$