A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute(rpm) to ensure proper mixing is close to :

(Take the radius of the drum to be 1.25 m and its axle to be horizontal) :

An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull F_G on the astronaut is :

A Carnot freezer takes heat from water at 0^oC inside it and rejects it to the room at a temperature of 27^oC. The latent heat of ice is 336×10³ J kg⁻¹. If 5 kg of water at 0^oC is converted into ice at 0^oC by the freezer, then the energy consumed by the freezer is close to :