# Q. The speed of sound through oxygen at T K is v m$s^{-1}$. As the temperature becomes 2T and oxygen gas dissociates into atomic oxygen, the speed of sound

ManipalManipal 2003Electromagnetic Waves

Solution:

## The rms velocity of sound in gas is $\hspace35mm v_{rms((molecule)} = \sqrt{\frac{\gamma RT}{M}}$ $\hspace40mm = \sqrt{\frac{1.4 \times RT}{M}} \hspace30mm ....(i)$ when the oxygen dissociates into atomic oxygen, its molecular mass becomes atomic mass, so, M $= \frac{M}{2}$ and $T = 2 T \, given \, and \, \gamma = 1.66$ $\hspace35mm v_{rms(atomic)} = \sqrt{\frac{1.66 \times R \times 2T}{M/2}}$ $\hspace50mm =\sqrt{\frac{1.66 \times R \times 2T \times 2}{M}} \hspace30mm ....(ii)$ From Eqs. (i) and (ii) $\frac{v_{rms(atomic)}}{v_{rms(molecule)}} = \sqrt{\frac{1.66 \times R \times 2T \times 2}{M}} \times \sqrt{\frac{M}{1.4 \times RT}}$ $\hspace40mm = \sqrt{\frac{1.66 \times 4}{1.4}} = 2.18$ Hence, $v_{rms(atomic)} = 2.18 \, v_{rms(molecule)}$ $\hspace40mm = 2 v_{rms(molecular)}$

You must select option to get answer and solution

## 1. The increase in pressure required to decrease the 200 L volume of a liquid by 0.004% (in kPa) is (Bulk modulus of the liquid ==2100 MPa)

Maharashtra CET 2006 Mechanical Properties Of Solids

## 2. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

AIPMT 1997 Gravitation

## 3. The diameter of a flywheel is increased by 1%. Increase in its moment of inertia about the central axis is

JIPMER 2015 System Of Particles And Rotational Motion

## 4. There are 26 tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives 3 beats with the next. The first one is octave of the last. What is the frequency of 18th tuning fork?

BHU 2005 Electromagnetic Waves

## 5. A body of mass 4 kg is accelerated upon by a constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is

KCET 2008 Laws Of Motion

## 6. A quarter horse power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be (in erg)

Manipal 2009 Work, Energy And Power

## 7. A cannon of mass I 000 kg, located at the base of an inclined plane fires a shelI of mass 100 kg in a horizontal direction with a velocity 180 $kmh^{-1}$. The angle of inclination of the inclined plane with the horizontal is 45$^{\circ}$. The coefficient of friction between the cannon and the inclined plane is 0.5. The height, in metre, to which the cannon ascends the inclined plane as a result of the recoiI is (g = 10 $ms^{-1})$

EAMCET 2004 Laws Of Motion

## 8. If voltage across a bulb rated 220 volt-100 watt drops by $2.5\%$ of its rated value, the percentage of the rated value by which the power would decrease is

AIPMT 2012 Current Electricity

## 9. Two charges $q_1$ and $q_2$ are placed 30 cm apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius 40cm from C to D. The change in the potential energy of the system is $\frac{q_3}{ 4 \pi \varepsilon_0}$ k. where k is

AIPMT 2005 Electrostatic Potential And Capacitance

## 10. Weight of a body of mass m decreases by 1% when it is raised to height h above the earth's surface. If the body is taken to a depth h in a mine, change in its weight is

KCET 2003 Gravitation