The escape velocity for earth is $$v$$. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

An electron and an alpha particle are accelerated by the same potential difference. Let $$\lambda_e$$ and $$\lambda_\alpha$$ denote the de-Broglie wavelengths of the electron and the alpha particle, respectively, then:

An object moving along horizontal $$x$$-direction with kinetic energy $$10 \mathrm{~J}$$ is displaced through $$x=(3 \hat{i}) \mathrm{m}$$ by the force $$\vec{F}=(-2 \hat{i}+3 \hat{j}) \mathrm{N}$$. The kinetic energy of the object at the end of the displacement $$x$$ is

An object falls from a height of $$10 \mathrm{~m}$$ above the ground. After striking the ground it loses $$50 \%$$ of its kinetic energy. The height upto which the object can rebounce from the ground is: