Question
Establish the formula for work in isothermal process.

Answer

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White coherent light $(400nm - 700nm)$ is sent through the slits of a Young's double slit experiment (figure.) The separation between the slits is $0.5mm$ and the screen is $50cm$ away from the slits. There is a hole in the screen at a point $1.0mm$ away (along the width of the fringes) from the central line.
  1. Which wavelength (s) will be absent in the light coming from the hole?
  2. which wavelength (s) will have a strong intensity?
A small block of superdense material has a mass of $3 \times 10^{24}kg$. It is situated at a height h (much smaller than the earth's radius) from where it falls on the earth's surface. Find its speed when its height from the earth's surface has reduced to $\frac{\text{h}}{2}.$ The mass of the earth is $6 \times 10^{24}kg$.
A ball moves along a curved path of radius 5m as shown in figure. It starts from point A and reaches point B. If there is no force of friction between the ball and surface of the path, then find the normal force that acts on the ball at the bottom (B) of the curved path.
To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \ kg$ moving with a speed $18.0 \ km / h$ on a smooth road and colliding with a horizontally mounted spring of spring constant $5.25 \times 10^3 N m ^{-1}$. What is the maximum compression of the spring?
Consider the above Example taking the coefficient of friction, $\mu,$ to be $0.5$ and calculate the maximum compression of the spring.
Mathematically describe the motion of a particle along a plane (or along a two-dimensional plane).
Calculate the temperature at which r.m.s. velocity of a gas molecule is the same as that of a molecule of another gas at 27°C. Molecular weight of first and second gases are 64 and 32 respectively.
Find the maximum magnifying power of a compound Microscope having a $25$ diopter lens as the objective, a $5$ diopter lens as the eyepiece and the separation $30cm$ between the two lenses. The least distance for clear vision is $25cm$.
Two balls having masses m and 2m are fastened to two light strings of same length (l). The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic.
  1. Find the velocities of the balls just after their collision.
  2. How high will the balls rise after the collision?
In figure k = 100N/m, M = 1kg and F = 10N,
  1. Find the compression of the spring in the equilibrium position.
  2. A sharp blow by some external agent imparts a speed of 2m/s to the block towards left. Find the sum of the potential energy of the spring and the kinetic energy of the block at this instant.
  3. Find the time period of the resulting simple harmonic motion.
  4. Find the amplitude.
  5. Write the potential energy of the spring when the block is at the left extreme.
  6. Write the potential energy of the spring when the block is at the right extreme.
The answers of (b), (e) and (f) are different. Explain why this does not violate the principle of conservation of energy.
You are riding in an automatic vehicle of mass 3000 kg . Assume that you are testing the oscillatory characteristics of the suspension system of this vechicle when the entire vehicle is placed on it, the suspended is inclined by 15 cm . Also, the amplitude of oscillation decreases by $50 \%$ in the period of one complete oscillation. Estimate the value of the following
(a) spring constant, and
(b) for the shock absorber system of a spring and $a$ wheel damping constant $b$.
Assume that each wheel carries a mass of 750 kg is.