A car of mass '$$m$$' moving with velocity '$$u$$' on a straight road in a straight line, doubles its velocity in time t. The power delivered by the engine of a car for doubling the velocity is

A bob of a simple pendulum of mass 'm' is displaced through 90$$^\circ$$ from mean position and released. When the bob is at lowest position, the tension in the string is

Let '$$\mathrm{W}_1$$' be the work done in blowing a soap bubble of radius '$$r$$' from soap solution at room temperature. The soap solution is now heated and second soap bubble of radius '$$2 r$$' is blown from the heated soap solution. If '$$W_2$$' is the work done in forming this bubble then

A cylindrical rod is having temperatures $$\theta_1$$ and $$\theta_2$$ at its ends. The rate of heat flow is '$$Q$$' $$\mathrm{J}{\mathrm{s}}^{-1}$$. All the linear dimensions of the rod are doubled by keeping the temperatures constant. What is the new rate of flow of heat?