The period of revolution of planet $A$ around the sun is $8$ times that of planet $B$. The distance of planet $A$ from the sun is how many times greater than that of planet $B$ from the sun?

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. If the angle of inclination of the plane is $60^{\circ}$,then the coefficient of friction is

$A$ bullet of mass $m$ strikes a block of mass $M$ connected to a light spring of stiffness $k,$ with a speed $v_0.$ If the bullet gets embedded in the block,then the maximum compression in the spring is

$3.65 \ g$ of $HCl$ is dissolved in $16.2 \ g$ of water. The mole fraction of $HCl$ in the resulting solution is

$A$ galvanometer,having a resistance of $50 \,\Omega$,gives a full-scale deflection for a current of $0.05 \,A$. The length in meters of a resistance wire of cross-sectional area $2.97 \times 10^{-2} \,cm^2$ that can be used to convert the galvanometer into an ammeter which can read a maximum of $5 \,A$ current is (Specific resistance of the wire = $5 \times 10^{-7} \,\Omega \cdot m$)