Question
If an automobile engine is overheated, it is cooled by putting water on it. It is advised that the water should be put slowly with engine running. Explain the reason.

Answer

In a hot engine the hot parts are expanded because of heat, if cold water is poured suddenly then there will be uneven thermal contraction in the parts. This will result in a stress to develop between the various parts of the engine and may let the engine to crack down.

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The three rods shown in figure, have identical geometrical dimensions. Heat flows from the hot end at a rate of $40$ Win the arrangement (a) Find the rates of heat flow when the rods are joined as in arrangement (b) and in (c) Thermal conductivities of aluminium and copper are $200Wm^{-1^\circ}C^{-1}$ and $400Wm^{-1^\circ}C^{-1}$ respectively.
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A small coin is placed on a record rotating at $33\frac{1}{3}$ rev/ minute. The coin does not slip on the record. Where does it get the required centripetal force from?
Read the passage given below and answer the following questions from 1 to 5. The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground by height h to that point against gravity. Let the work done on the object against gravity be W. That is, work done, W = force × displacement = mg × h Therefore potential energy (PE) = mg*h. The dimensions of potential energy are $[ML^2T^{-2}]$ and the unit is joule (J), the same as kinetic energy or work. To reiterate, the change in potential energy, for a conservative force, $\triangle\text{V}$ is equal to the negative of the work done by the force $\triangle\text{v}=−\text{F}(\text{x})\triangle\text{x}.$ Conservation of mechanical energy: Suppose that a body undergoes displacement $\triangle\text{x}$ under the action of a conservative force F. Then from the WE theorem we have, $ \triangle\text{K}=\text{F}(\text{x})\triangle\text{x}$ If the force is conservative, the potential energy function V(x) can be defined such that $-\triangle\text{V}=\text{F}(\text{x})\triangle\text{x}$ The above equations imply that $\triangle\text{K}+\triangle\text{V}=0$ or $\triangle(\text{K}+\text{V})=0.$ Which means that K + V, the sum of the kinetic and potential energies of the body is a constant? Over the whole path, $x_i$ to $x_f$, this means that $K_i + V(x_i ) = Kf + V(x_f )$. The quantity K +V(x), is called the total mechanical energy of the system. Individually the kinetic energy K and the potential energy V(x) may vary from point to point, but the sum is a constant. The aptness of the term ‘conservative force’ is now clear. Let us consider some of the definitions of a conservative force.
  • A force F(x) is conservative if it can be derived from a scalar quantity V(x).
  • The work done by the conservative force depends only on the end points. This can be seen from the relation, W = Kf – Ki = V (xi ) – V(xf ) which depends on the end points.
  • A third definition states that the work done by this force in a closed path is zero. This is once again apparent since xi = xf .
Thus, the principle of conservation of total mechanical energy can be stated as the total mechanical energy of a system is conserved if the forces, doing work on it, are conservative.
  1. Dimensions of potential energy is given by:
  1. $[ML^2T^{-2}]$
  2. $[M^2 L^2T^{-2}]$
  3. $[ML^3T^{-3}]$
  4. None of the above
  1. SI unit of potential energy is:
  1. Joule(J)
  2. Newton meter(N-m)
  3. Both a and b
  4. None of these
  1. Define the gravitational potential energy.
  1. Define conservative force.
  1. State conservation of mechanical energy.
A dimensionless quantity:
  1. Never has a unit.
  2. Always has a unit
  3. May have a unit.
  4. Does not exist.
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  1. equation of motions are applicable to motion with
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  2. non uniform acceleration
  3. constant velocity
  4. none of these
  1. There are $4$ equation of motion. True or false?
  1. True
  2. False
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Consider a gravity-free hall in which an experimenter of mass $50kg$ is resting on a $5kg$ pillow, 8ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of $8ft/s$. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process.
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A metallic loop is placed in a nonuniform magnetic field. Will an emf be induced in the loop?