Q8. A diatomic gas $( \gamma = 1.4 )$ does 100 J of work in an isobaric expansion. The heat given to the gas is :
(1) 250 J
(2) 150 J
(3) 350 J
(4) 490 J

Q8. A sample of 1 mole gas at temperature $T$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma = \frac { 3 } { 2 }$, then the work done by the gas in the process is:
(1) $\frac { R } { T } [ 2 - \sqrt { 2 } ]$
(2) $\frac { T } { R } [ 2 + \sqrt { 2 } ]$
(3) RT $[ 2 - \sqrt { 2 } ]$
(4) $\mathrm { RT } [ 2 + \sqrt { 2 } ]$

Q8. The temperature of a gas is $- 78 ^ { \circ } \mathrm { C }$ and the average translational kinetic energy of its molecules is K . The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is :
(1) $127 ^ { \circ } \mathrm { C }$
(2) $117 ^ { \circ } \mathrm { C }$
(3) $- 39 ^ { \circ } \mathrm { C }$
(4) $- 78 ^ { \circ } \mathrm { C }$

Q9. The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400 ^ { \circ } \mathrm { C }$, the resistance of platinum wire is :
(1) $10 \Omega$
(2) $8 \Omega$
(3) $16 \Omega$
(4) $2 \Omega$

Q9. The translational degrees of freedom ( $f _ { t }$ ) and rotational degrees of freedom ( $f _ { r }$ ) of $\mathrm { CH } _ { 4 }$ molecule are:
(1) $f _ { t } = 2$ and $f _ { r } = 2$
(2) $f _ { t } = 3$ and $f _ { r } = 3$
(3) $f _ { t } = 3$ and $f _ { r } = 2$
(4) $f _ { t } = 2$ and $f _ { r } = 3$

Q9. Match List I with List II :

List I

(A) Kinetic energy of planet
(B) Gravitation Potential energy of sun-planet system
(C) Total mechanical energy of planet
(D) Escape energy at the surface of planet for unit mass object

List II

(I) $- \mathrm { GMm } / \mathrm { a }$ (II) $\mathrm { GMm } / 2 \mathrm { a }$ (III) $\frac { \mathrm { Gm } } { \mathrm { r } }$ (IV) $- \mathrm { GMm } / 2 \mathrm { a }$ (Where $\mathbf { a } =$ radius of planet orbit, $\mathbf { r } =$ radius of planet, $\mathrm { M } =$ mass of Sun, $\mathrm { m } =$ mass of planet) Choose the correct answer from the options given below :
(1) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(2) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(3) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(4) (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Q9. If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :
(1) $\sqrt { 2 } n \pi d ^ { 2 }$
(2) $\frac { 1 } { \sqrt { 2 n \pi d ^ { 2 } } }$
(3) $\frac { 1 } { \sqrt { 2 } n \pi d ^ { 2 } }$
(4) $\frac { 1 } { \sqrt { 2 } n ^ { 2 } \pi ^ { 2 } d ^ { 2 } }$

Q9. A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:
(1) $\frac { 1 } { 32 }$
(2) $\frac { 2 \sqrt { 2 } } { 1 }$
(3) $\frac { 1 } { 2 \sqrt { 2 } }$
(4) $\frac { 1 } { 4 }$

Q9. Energy of 10 non rigid diatomic molecules at temperature $T$ is :
(1) $70 \mathrm {~K} _ { \mathrm { B } } \mathrm { T }$
(2) $35 \mathrm {~K} _ { \mathrm { B } } \mathrm { T }$
(3) $\frac { 7 } { 2 } \mathrm { RT }$
(4) 35 RT

Q9. Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The [Figure] relation between the ratio $\frac { V _ { a } } { V _ { d } }$ and the ratio $\frac { V _ { b } } { V _ { c } }$ is:
(1) $\frac { V _ { a } } { V _ { d } } \neq \frac { V _ { b } } { V _ { c } }$
(2) $\frac { V _ { a } } { V _ { d } } = \frac { V _ { b } } { V _ { c } }$
(3) $\frac { V _ { a } } { V _ { d } } = \left( \frac { V _ { b } } { V _ { c } } \right) ^ { - 1 }$
(4) $\frac { V _ { a } } { V _ { d } } = \left( \frac { V _ { b } } { V _ { c } } \right) ^ { 2 }$

Q9. Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the options given below :
(1) Statement I is true but Statement II is false
(2) Both Statement I and Statement II are false
(3) Both Statement I and Statement II are true
(4) Statement I is false but Statement II is true

Q9. The volume of an ideal gas ( $\gamma = 1.5$ ) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:
(1) $\frac { 16 } { 25 }$
(2) $\frac { 4 } { 5 }$
(3) $\frac { 8 } { 5 \sqrt { 5 } }$
(4) $\frac { 2 } { \sqrt { 5 } }$

Q9. Five charges $+ q , + 5 q , - 2 q , + 3 q$ and $- 4 q$ are situated as shown in the figure. The electric flux due to this [Figure] configuration through the surface $S$ is :
(1) $\frac { 4 q } { \epsilon _ { 0 } }$
(2) $\frac { 5 q } { \epsilon _ { 0 } }$
(3) $\frac { q } { \epsilon _ { 0 } }$
(4) $\frac { 3 q } { \epsilon _ { 0 } }$

Q10. On celcius scale the temperature of body increases by $40 ^ { \circ } \mathrm { C }$. The increase in temperature on Fahrenheit scale is
(1) $68 ^ { \circ } \mathrm { F }$
(2) $75 ^ { \circ } \mathrm { F }$
(3) $72 ^ { \circ } \mathrm { F }$
(4) $70 ^ { \circ } \mathrm { F }$

Q10. In simple harmonic motion, the total mechanical energy of given system is $E$. If mass of oscillating particle $P$ [Figure] is doubled then the new energy of the system for same amplitude is:
(1) $E$
(2) $E / \sqrt { 2 }$
(3) $2 E$
(4) $E \sqrt { } \overline { 2 }$

Q10. Given below are two statements : Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $0 ^ { \circ }$. Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. In the light of the above statement, choose the correct answer from the options given below.
(1) Both Statement I and Statement II are false
(2) Both Statement I and Statement II are true
(3) Statement I is false but Statement II is true
(4) Statement I is true and Statement II is false

Q10. The vehicles carrying inflammable fluids usually have metallic chains touching the ground :
(1) To protect tyres from catching dirt from ground
(2) To alert other vehicles
(3) It is a custom
(4) To conduct excess charge due to air friction to ground and prevent sparking

Q10. The specific heat at constant pressure of a real gas obeying $P V ^ { 2 } = R T$ equation is:
(1) $\frac { R } { 3 } + C _ { V }$
(2) $C _ { V } + R$
(3) $C _ { V } + \frac { R } { 2 V }$
(4) $R$

Q10. Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force 16 N . A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between P and S is :
(1) 1 N
(2) 6 N
(3) 12 N
(4) 4 N

Q10. A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $\left( 27 ^ { \circ } \mathrm { C } \right)$. The ratio of specific heat of gases at constant volume respectively is:
(1) $\frac { 7 } { 5 }$
(2) $\frac { 3 } { 5 }$
(3) $\frac { 5 } { 3 }$
(4) $\frac { 3 } { 2 }$

Q10. A plane progressive wave is given by $y = 2 \cos 2 \pi ( 330 \mathrm { t } - x ) \mathrm { m }$. The frequency of the wave is:
(1) 330 Hz
(2) 660 Hz
(3) 340 Hz
(4) 165 Hz

Q10. A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:
(1) increases
(2) decreases
(3) remains same
(4) becomes zero

Q10. The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be [Figure]
(1) $\frac { 8 R } { 3 }$
(2) $\frac { 5 R } { 3 }$
(3) $\frac { 4 R } { 3 }$
(4) $\frac { 2 } { 3 } R$

Q11. P-T diagram of an ideal gas having three different densities $\rho _ { 1 } , \rho _ { 2 } , \rho _ { 3 }$ (in three different cases) is shown in the [Figure] figure. Which of the following is correct :
(1) $\rho _ { 1 } > \rho _ { 2 }$
(2) $\rho _ { 2 } < \rho _ { 3 }$
(3) $\rho _ { 1 } = \rho _ { 2 } = \rho _ { 3 }$
(4) $\rho _ { 1 } < \rho _ { 2 }$

Q11. A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:
(1) $\frac { q } { 2 \epsilon _ { 0 } }$
(2) $\frac { q } { 8 \epsilon _ { 0 } }$
(3) Zero
(4) $\frac { q } { 4 \epsilon _ { 0 } }$