Question
What is a heat engine? What are its essential parts? Explain its principle and establish the formula for its efficiency.
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Answer
SELF
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Three blocks are connected as shown on a horizontal frictionless table, and pulled to the right with a force of $T_3 = 60N$. 
If $m_1 = 10kg, m_2 = 20kg$ and $m_3 = 30kg$. Prove that $\frac{\text{T}_1}{\text{T}_2}=\frac{1}{3}.$
→If $m_1 = 10kg, m_2 = 20kg$ and $m_3 = 30kg$. Prove that $\frac{\text{T}_1}{\text{T}_2}=\frac{1}{3}.$
Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar. Consider a plane making an angle $\Delta$ with the length. What are the tensile and shearing stresses on this plane?
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- For what angle is the tensile stress a maximum?
- For what angle is the shearing stress a maximum?
Consider a situation similar to that of the previous problem except that the ends of the rod slide on a pair of thick metallic rails laid parallel to the wire. At one end the rails are connected by resistor of resistance R.
- What force is needed to keep the rod sliding at a constant speed v?
- In this situation what is the current in the resistance R?
- Find the rate of heat developed in the resistor.
- Find the power delivered by external agent exerting the force on the rod.
When the sun is directly overhead, the surface of the earth receives $1.4 \times 10^3 W m^{-2}$ of sunlight. Assume that the light is monochromatic with average wavelength $500nm$ and that no light is absorbed in between the sun and the earth's surface. The distance between the sun and the earth is $1.5 \times 10^{11}m$.
→- Calculate the number of photons falling per second on each square metre of earth's surface directly below the sun.
- How many photons are there in each cubic metre near the earth's surface at any instant?
- How many photons does the sun emit per second?
A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite $=200 \mathrm{~kg}$; mass of the earth $=6.0 \times$ $10^{24} \mathrm{~kg}$; radius of the earth $=6.4 \times 10^6 \mathrm{~m} ; \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$.
→The friction coefficient between the table and the block shown in figure is 0.2. Find the tensions in the two strings.
Two identical balls A and B undergo a perfectly elastic two dimensional collision. Initially A is moving with a speed of $10ms^{-1}$ and B is at rest. Due to collision A is scattered through angle of $30°$. What are the speed of A and B after the collision?
→Explain two-dimensional motion by giving an example. Explain the displacement, velocity and acceleration of a particle in two-dimensional motion
An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that $\text{T}=\frac{\text{k}}{\text{R}}\sqrt{\frac{\text{r}^3}{\text{g}}},$ where k is a dimensionless constant and g is acceleration due to gravity.
→A ball of mass $100g$ and having a charge of $4.9 \times 10^{-5}C$ is released from rest in a region where a horizontal electric field of $2.0 \times 10^4NC^{-1}$ exists.
→- Find the resultant force acting on the ball.
- What will be the path of the ball?
- Where will the ball be at the end of $2s$?