The ratio of the acceleration for a solid sphere (mass $$m$$ and radius $$R$$) rolling down an incline of angle '$$\theta$$' without slipping down the incline without rolling is.

The de-Broglie wavelength of a proton $$\left(m=1.67 \times 10^{-27} \mathrm{~kg}\right)$$ acclerated through a potential difference of $$2 \mathrm{~kV}$$ is

The frequency of a sonometer wire is $$100 \mathrm{~Hz}$$ When the weights producing the tensions are completely immersed in water, the frequence becomes $$60 \mathrm{~Hz}$$ and on immersing the weights in a certain liquid, the frequency becomes $$40 \mathrm{~Hz}$$. The specific gravity of the liquid is

A particle of mass $m$ is projected with a velocity $$v$$ making an angle of $$45^{\circ}$$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $$h$$ is.