A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n² R t² where n is a constant. The power delivered to the particle by the force acting on it, is :

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 :

The resistance of an electrical toaster has a temperature dependence given by R(T) = R₀ [1 + $$\alpha $$(T − T₀)] in its range of operation. At T₀ = 300 K, R = 100 $$\Omega $$ and at T = 500 K, R = 120 $$\Omega $$. The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is :