Level – I

Q:1. A meter washer has a hole of diameter d_{1} and an external diameter d_{2} , where 3d_{2} = d_{1}. On heating, d_{2} increases by 0.3%. Then d_{1} will

(a) decrease by 0.1%

(b) decrease by 0.3%

(c) increase by 0.1%

(d) increase by 0.3%

Q:2.If I is the moment of inertia of a solid body, the change in l corresponding to a small change in temperature is

(a) αIΔT

(b) (1/2)αIΔT

(c) 2αIΔT

(d) 3αIΔT

Q:3.If α is the coefficient of linear expansion, the change in the period t of a physical pendulum with temperature change of ΔT is

(a) (1/2) αtΔT

(b) (1/4) αtΔT

(c) (3/4) αtΔT

(d) (1/3) αtΔT

Q:4. A steel scale is to be prepared such that the millimeter intervals are to be accurate within 6 x 10^{-5} mm . The maximum temperature variation during the ruling of the millimeter marks (α =12 x 10^{-6} C^{-1}) is

(a) 4.0ºC

(b) 4.5ºC

(c) 5.0ºC

(d) 5.5ºC

Q:5. A block of ice at –10ºC is slowly heated and converted to steam at 100ºC. Which of the following curves represents the phenomenon qualitatively ?

(a)

(b)

(c)

(d)

Q:6. A point source of heat of power P is placed at the center of a spherical shell of mean radius R. The material of the shell has thermal conductivity k. If the temperature difference between the outer and the inner surface of the shell is not to exceed T, then the thickness of the shell should not be less than

(a)$ \displaystyle \frac{2 \pi R^2 k T}{P} $

(b)$ \displaystyle \frac{4 \pi R^2 k T}{P} $

(c)$ \displaystyle \frac{ \pi R^2 k T}{P} $

(d)$ \displaystyle \frac{\pi R^2 k T}{4 P} $

Q:7. Three rods A, B and C have the same dimensions. Their thermal conductivities are and respectively. A and B are placed end to end, with their free ends kept at a certain temperature difference. C is placed separately, with its ends kept at the same temperature difference. The two arrangements conduct heat at the same rate. must be equal to

(a)$ \displaystyle k_A + k_B $

(b)$ \displaystyle \frac{k_A k_B}{k_A + k_B} $

(c)$ \displaystyle \frac{1}{2}(k_A + k_B) $

(d)$ \displaystyle \frac{2 k_A k_B}{k_A + k_B} $

Q:8. A cyclic process is shown in the p-T diagram. Which of the curves show the same process on a V-T diagram ?

(a)

(b)

(c)

(d)

Q:9. A solid at temperature T_{1} is kept in an evacuated chamber at temperature . The rate of increase of temperatrue of the body is proportional to

(a) T_{2} – T_{1}

(b) T_{2}^{2} – T_{1}^{2}

(c) T_{2}^{4} – T_{1}^{4}

(d) T_{2}^{3} – T_{1}^{3}

Q:10. 70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30ºC to 35ºC. The amount of heat required in calories to raise the temperature of same gas through the same range (30ºC to 35ºC) at constant volume is

(a) 30

(b) 50

(c) 70

(d) 90.

### Answer:

1.(d) 2.(c) 3.(a) 4.(c)

5.(a) 6.(b) 7.(b) 8.(c)

9.(c) 10.(b)

Q:11. A black body radiates power P and maximum energy is radiated by it around a wavelength λ_{o }. The temperature of the black body is now changed such that it radiated maximum energy around the wavelength 3λ_{o}/4 . The power radiated by it now is

(a) 256P/81

(b) 16P/9

(c) 64P/27

(d) 4P/3

Q:12. Five rods having thermal conductivities k_{1} , k_{2} , k_{3} , k_{4} and k_{5} are arranged as shown. The points A and B are maintained at different temperature such that no thermal current flows through the central rod.

(a)k_{1}k_{4} = k_{2}k_{3}

(b)k_{1} = k_{3} , k_{2} = k_{4}

(c)k_{1}k_{3} = k_{2}.k_{4}

(d)k_{1}/k_{4} = k_{3} / k_{2}

Q:13. An ideal gas expands according to the law pV^{2}= const. The molar heat capacity C is

(a)C_{v} + R

(b)C_{v} – R

(c)C_{v} + 2R

(d)C_{v} – 3R

Q:14.If W_{1} is the work done in compressing an ideal gas from a given initial state through a certain volume isothermally and W_{2} is the work done in compressing the same gas from the same initial state through the same volume adiabatically, then

(a)W_{1} = W_{2}

(b)W_{1} < W_{2}

(c)W_{1} > W_{2}

(d)W_{1} = 2W_{2}

Q:15. The rate of emission of a black body at 0ºC is R. Its rate of emission at 273ºC is

(a) 4R

(b) 8R

(c) 16R

(d) 32R

Q:16. A body emits radiation when its temperature is

(a) >0ºC

(b) >100ºC

(c) > surrounding temperature

(d) it emits radiation at all temperatures (T > 0ºK)

Q:17. Radiation from a black body at the thermodynamic temperature T_{1} is measured by a small detector at distance d_{1} from it. When the temperature is increased to T_{2} and the distance to d_{2} , the power received by the detector is unchanged. What is the ratio d_{2}/d_{1} ?

(a)T_{2}/T_{1}

(b)(T_{2}/T_{1})^{2}

(c)(T_{1}/T_{2})^{2}

(d)(T_{2}/T_{1})^{4}

Q:18 . Two identical containers joined by a small pipe initially contain the same gas at pressure p_{o} and absolute temperature T_{o} . One container is now maintained at the same temperature while the other is heated to 2T_{o} . The common pressure of the gases will be

(a) 2p_{o}/3

(b) 4p_{o}/3

(c) 5p_{o}/3

(d) 2p_{o}

Q:19. An ideal gas changes from state a to state b as shown in figure. What is the work done by the gas in the process ?

(a) zero

(b) positive

(c) negative

(d) infinite

Q:20. The weight of a person is 60 kg. If he gets one kilo-calorie of heat through food and the efficiency of his body is 28%, then upto how much height he can climb ? Take g = 10 m s-2

(a) 100 cm

(b) 196 cm

(c) 400 cm

(d) 1000 cm.

###### Answer.

11. (a) 12. (a) 13 (b) 14. (b)

15. (c) 16. (d) 17. (b) 18. (b)

19. (a) 20. (b)