Consider a uniform rod of mass M = 4m and length $$\ell $$ pivoted about its centre. A mass m moving with velocity v making angle $$\theta = {\pi \over 4}$$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :

The dimension of stopping potential V₀ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :

Consider a solid sphere of radius R and mass density
$$\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$ , $$0 < r \le R$$
The minimum density of a liquid in which it will float is :

Consider two solid spheres of radii R₁ = 1m, R₂ = 2m and masses M₁ and M₂, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $${{{M_1}} \over {{M_2}}}$$ is :