An object with a mass $10 \ kg$ moves at a constant velocity of $10 \ m/s$. $A$ constant force then acts for $4 \ s$ on the object and gives it a speed of $2 \ m/s$ in the opposite direction. The impulse acting on the object is ........ $N \cdot s$.

$A$ tiny air bubble in a glass slab $(\mu = 1.5)$ appears from one side to be $6\, cm$ from the glass surface and from the other side,$4\, cm$. The thickness of the glass slab is......$cm$

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

The ratio of the de-Broglie wavelength of an $\alpha$-particle to that of a proton,when both are subjected to the same magnetic field such that the radii of their paths are equal,assuming the magnetic field induction vector $\overrightarrow{B}$ is perpendicular to the velocity vectors of both particles,is:

The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1 : 2$ and their lengths are in the ratio $2 : 1$. If the temperature difference between their ends is the same,the ratio of the rates of flow of heat through them will be

Which one of the following conditions correctly describes the manner of determining the sex?