SECTION-A

- A brass rod and lead rod each 80 cm long at 0
^{°}C are clamped together at one end with their free ends coinciding. If the system is placed in a steam bath then the separation of free ends of the rods is:

(α _{Brass} = 18 × 10 ^{–6}/^{°}C and α _{Lead} = 28 × 10^{-6}/^{°}C)

(1) 0.2 mm

(2) 0.8 mm

(3) 1.4 mm

(4) 1.6 mm

- A person weighing 50 kg takes in 1500 k Cal diet per day. If this energy were to be used in heating the body of person without any losses, then the rise in his temperature is

(specific heat of human body = 0.83 cal g ^{–1} C ^{–1})?

(1) 30^{o}C

(2) 48^{o}C

(3) 40.16^{o}C

(4) 36.14^{o}C

- A solid sphere and a hollow sphere of same material and size are heated to same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is T, then:

(1) the hollow sphere will cool at a faster rate for all values of T.

(2) the solid sphere will cool at a faster rate for all values of T

(3) both spheres will cool at the same rate for all values of T

(4) both spheres will cool at the same rate only for small values of T.

- If the pressure of an ideal gas contained in a closed vessel increased by 0.5%, the increase in temperature is 2 K. The initial temperature of the gas is :-

(1) 27^{°}C

(2) 127^{°}C

(3) 300^{°}C

(4) 400^{°}C

- Heat is supplied to a diatomic gas at constant pressure. The ratio of ΔQ : ΔU : ΔW is :-

(1) 5 : 3 : 2

(2) 5 : 2 : 3

(3) 7 : 5 : 2

(4) 7 : 2 : 5

- A carnot engine, having an efficiency of η = 1/10 as heat engine is used as a refrigerator. If the work done on the system is 10 J, then amount of energy rejected to the reservoir at higher temperature is :-

(1) 99 J

(2) 100 J

(3) 1 J

(4) 90 J

- The co-efficient of volume expansion of glycerine is 49 × 10
^{–5}/^{°}C, then what will be fractional change in its density (approx) for 30^{°}C rise in temperature.

(1) 1.5 × 10^{–2}

(2) 2.5 × 10^{–2}

(3) 2.0 × 10^{–2}

(4) 2.8 × 10^{–2}

- A body cools from 75
^{°}C to 72^{°}C in time t_{1}from 72^{°}C to 69^{°}C in t_{2}and from 69^{°}C to 66^{°}C in t_{3}, then :-

(1) t_{3} > t_{2} > t_{1}

(2) t_{1} > t_{2} > t_{3}

(3) t_{2} > t_{1} = t_{3}

(4) t_{1} > t_{2} < t_{3}

- Molecular hydrogen at one atmosphere and helium at two atmospheres occupy volume V each at the same temperature. The rms velocity of hydrogen molecules is x times the rms velocity of helium molecules. What is the value of x?

(1) 1

(2) 2

(3) 2

(4) 3

- The maximum wavelength of radiation emitted at 200 K is 40 μm. What will be the maximum wavelength of radiation emitted at 2400 K ?

(1) 3.33 μm

(2) 0.66 μm

(3) 1 μm

(4) 1 m

- A Carnot engine operates with source at 127ºC and sink at 27ºC. If the source supplies 16 kJ of heat energy, the work done by the engine is:-

(1) 30 kJ

(2) 10 kJ

(3) 4 kJ

(4) 1 kJ

- The lengths of two metallic rods at temperatures θ are L
_{A}and L_{B}and their linear coefficient of expansion are α_{A}and α_{B}respectively. If the difference in their lengths is to remain constant at any temperature, then

(1) L_{A}/L_{B} = α_{A}/α_{B}

(2) L_{A}/L_{B} = α_{B}/α_{A}

(3) α_{A} = α_{B}

(4) α_{A}α_{B} = 1

- The mean kinetic energy of a gas at 300 K is 100 J. The mean energy of the gas at 450 K is equal to :-

(1) 100 J

(2) 3000 J

(3) 450 J

(4) 150 J

- One kg of a diatomic gas is at a pressure of 8×104 N/m2. The density of the gas is 4 kg/m
^{3}. What is the energy of the gas due to its thermal motion :-

(1) 3 × 10^{4} J

(2) 5 × 10^{4} J

(3) 6 × 10^{4} J

(4) 7 × 10^{4} J

- A particle executes SHM of type x = asinωt. It takes time t
_{1}from x = 0 to x = and t_{2 }from x = to x = a. The ratio of t_{1}: t_{2}will be :-

(1) 1 : 1

(2) 1 : 2

(3) 1 : 3

(4) 2 : 1

- The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes 8 cm/s, will be

(1) 2√3cm

(2) √3 cm

(3) 1cm

(4) 2cm

- A body of mass 1 kg is executing simple harmonic motion. Its displacement y (cm) at t seconds is given by y = 6 sin(100t + π/4) . Its maximum kinetic energy is

(1) 6 J

(2) 18 J

(3) 24 J

(4) 36 J

- A mass m is suspended from a weightless spring and it has time-period ‘T’. The spring is now divided into four equal parts and the same mass is suspended from one of these parts. The now time period will be :-

(1) T

(2) T/2

(3) 2T

(4) T/4

- A simple pendulum suspended from the roof of a lift oscillates with frequency υ when the lift is at rest. If the lift falls freely under gravity, its frequency of oscillation becomes:-

(1) zero

(2) υ

(3) 2υ

(4) infinite

- The displacement of a particle in SHM varies according to the relation x = 4 (cos πt + sinπt). The amplitude of the particle is :-

(1) –4

(2) 4

(3) 4

(4) 8

- The particle executing simple harmonic motion has a kinetic energy K
_{o }cos^{2 }ωt. The maximum values of the potential energy and the total energy are respectively :-

(1) K_{o }and K_{o}

(2) 0 and 2K_{o}

(3)

(4) K_{o} and 2K_{o}

30. Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has a amplitude that is twice that of wave B and transmits energy at rate that is ______ that of wave B.

(1) half

(2) twice

(3) one-fourth

(4) four times

31. The frequency of man’s voice is 300 Hz and its wavelength is 1 meter. If the wavelength of a child’s voice is 1.5m, then the frequency of the child’s voice is :-

(1) 200 Hz

(2) 150 Hz

(3) 400 Hz

(4) 450 Hz

- Two liquids A and B at 30°C and 20°C respectively. When equal mass of there is mixed final temperature is 26°C then ratio of their specific heat is :-

(1) 4 : 3

(2) 3 : 4

(3) 2 : 3

(4) 3 : 2

- Temperature of a piece of iron is 27°C and it is radiating energy at the rate of Q kWm
^{-2}. If its temperature is raised to 151°C, the rate of radiation of energy will become approximately: –

(1) 2Q kWm^{2}

(2) 4Q kWm^{2}

(3) 6Q kWm^{2}

(4) 8Q kWm^{2}

- The thermodynamic variables of a jar filled with gas A are P, V and T and another jar B filled with another gas are 2P, V/4 and 2T, where the symbols have their usual meaning. The ratio of the number of molecules of jar A to those of jar B is :

(1) 4 : 1

(2) 2 : 1

(3) 1 : 2

(4) 1 : 1

- A tuning fork gives 4 beats with 50 cm length of a sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is :-

(1) 404 Hz

(2) 400 Hz

(3) 396 Hz

(4) 384 Hz

- When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

(1) More frequency, less wavelength

(2) More frequency, more wavelength

(3) Less frequency, less wavelength

(4) More frequency, constant wavelength

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