A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10^–12 m, the minimum electron energy required is close to -

A plano convex lens of refractive index $$\mu $$₁ and focal length ƒ₁ is kept in contact with another plano concave lens of refractive index $$\mu $$₂ and focal length ƒ₂. If the radius of curvature of their spherical faces is R each and ƒ₁ = 2ƒ₂, then $$\mu $$₁ and $$\mu $$₂ are related as -

A uniform metallic wire has a resistance of 18 $$\Omega $$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -