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Physics - Section A

1.

The variation of acceleration,\(a~\) of a particle executing SHM with displacement \(x~\) is:

1.		2.
3.		4.

2.

A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them will be:
1.$\frac{\mathrm{\pi }}{3}$
2.$\frac{2\mathrm{\pi }}{3}$
3.$\frac{\mathrm{\pi }}{6}$
4.$\frac{\mathrm{\pi }}{2}$

3.

In a given process, dW = 0, dQ < 0, then for the gas:
1. Temperature increases
2. Volume decreases
3. Pressure decreases
4. Pressure increases

4.

5.

When two displacements represented by y₁=asin(ωt) and y₂=bcos(ωt) are superimposed,the motion is -
(1) not a simple harmonic
(2) simple harmonic with amplitude a/b
(3) simple harmonic with amplitude$\sqrt{a^2+b^2}$
(4) simple harmonic with amplitude (a+b)/2

6.

The number of possible natural oscillations of the air column in a pipe closed at one endof a length of 85 cm whose frequencies lie below 1250 Hz is: (velocity of sound 340ms^-1)

7.

8.

Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to the occurrence of 6 beats/s when both thewires oscillate together would be:

9.

In thermodynamic processes, which of the following statements is not true?

10.

A simple pendulum hanging from the ceiling of a stationary lift has a time period T₁. When the lift moves downward with constant velocity, then the time period becomesT₂.It can be concluded that:

11.

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire is A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to -
(1)$2\mathrm{\pi }\left(\frac{\mathrm{m}}{\mathrm{K}}\right)$
(2) $2\mathrm{\pi }{\left\{\frac{\left(\mathrm{YA}+\mathrm{KL}\right)\mathrm{m}}{\mathrm{YAK}}\right\}}^{1/2}$
(3) $2\mathrm{\pi }\frac{\mathrm{mYA}}{\mathrm{KL}}$
(4) $2\mathrm{\pi }\frac{\mathrm{mL}}{\mathrm{YA}}$

12.

The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is

(1) 1$\times$10² N/m
(2)150 N/m
(3) 0.667$\times$ 10² N/m
(4) 3$\times$ 10² N/m

13.

The distance between two consecutive crests in a wave train produced in a string is 5 cm. If 2 complete waves pass through any point per second, the velocity of the wave is :
1. 10 cm/sec
2. 2.5 cm/sec
3. 5 cm/sec
4. 15 cm/sec

14.

The phase difference between two points separated by 1m in a wave of frequency 120 Hz is 90°. The wave velocity is :
1. 180 m/s
2. 240 m/s
3. 480 m/s
4. 720 m/s

15.

The velocity of sound in air is:

16.

The type of waves that can be propagated through solid is :
(1) Transverse
(2) Longitudinal
(3) Both (1) and (2)
(4) None of these

17.

The equation of a progressive wave is given by $y=4\sin \left\{\pi \left(\frac{{\displaystyle t}}{{\displaystyle 5}}-\frac{{\displaystyle x}}{{\displaystyle 9}}\right)+\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right\}$.
Which of the following is correct​​​​?
1.v = 5 m / sec
2.λ = 18 m
3.a = 0.04 m
4.n = 50 Hz

18.

A simple harmonic progressive wave is represented by the equation : $y=8\sin 2\pi (0.1x-2t)$ where x and y are in cm and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the x-direction is :
(1) 18°
(2) 36°
(3) 54°
(4) 72°

19.

Two waves represented by the following equations are travelling in the same medium $y_1=5\sin 2\pi (75t-0.25x)$, $y_2=10\sin \pi (150t-0.50x)$
The intensity ratio I₁/I₂ of the two waves is :
(1) 1 : 2
(2) 1 : 4
(3) 1 : 8
(4) 1 : 16

20.

Two sound waves of wavelengths 5m and 6m formed 30 beats in 3 seconds. The velocity of sound is :
(1) 300 ms^–1
(2) 310 ms^–1
(3) 320 ms^–1
(4) 330 ms^–1

21.

A string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is :
(1) $\frac{l}{4}$
(2) $\frac{l}{2}$
(3) l
(4) 2l

22.

Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is :
(1) 5
(2) 8
(3) 6
(4) 10

23.

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. The tension of the string remaining constant the frequency of the second tuning fork is :
(1) 163.84 Hz
(2) 400 Hz
(3) 320 Hz
(4) 204.8 Hz

24.

If the velocity of sound in air is 350 m/s. Then the fundamental frequency of an open organ pipe of length 50 cm, will be
(1) 350 Hz
(2) 175 Hz
(3) 900 Hz
(4) 750 Hz

25.

Two whistles A and B produce notes of frequencies 660 Hz and 596 Hz respectively. There is a listener at the mid-point of the line joining them. Now the whistle B and the listener start moving with speed 30 m/s away from the whistle A. If the speed of sound be 330 m/s, how many beats will be heard by the listener:
(1) 2
(2) 4
(3) 6
(4) 8

26.

A thermo-dynamical system is changed from state (P₁, V₁) to (P₂, V₂) by two different process. The quantity which will remain same will be
(1) ΔQ
(2) ΔW
(3) ΔQ + ΔW
(4) ΔQ – ΔW

27.

In a thermodynamic process, pressure of a fixed mass of a gas is changed in such a manner that the gas molecules absorb 30 J of heat and 10 J of work is done by the gas. If the initial internal energy of the gas was 40 J, then the final internal energy will be -
(1) 30 J
(2) 20 J
(3) 60 J
(4) 40 J

28.

A vessel containing 5 litres of a gas at 0.8 m pressure is connected to an evacuated vessel of volume 3 litres. The resultant pressure inside will be (assuming whole system to be isolated)
(1) 4/3 m
(2) 0.5 m
(3) 2.0 m
(4) 3/4 m

29.

The latent heat of vaporisation of water is 2240 J/gm. If the work done in the process of expansion of 1 g is 168 J, then increase in internal energy is
(1) 2408 J
(2) 2240 J
(3) 2072 J
(4) 1904 J

30.

In adiabatic expansion
(1) ΔU = 0
(2) ΔU = negative
(3) ΔU = positive
(4) ΔW = zero

31.

The pressure and density of a diatomic gas $(\gamma =7/5)$ changes adiabatically from (P, d) to (P', d'). If $\frac{d\text{'}}{d}=32$, then $\frac{P\text{'}}{P}$ should be:

32.

One mole of helium is adiabatically expanded from its initial state $(P_i,V_i,T_i)$ to its final state $(P_f,V_f,T_f)$. The decrease in the internal energy associated with this expansion is equal to
(1) $C_V(T_i-T_f)$
(2) $C_P(T_i-T_f)$
(3) $\frac{1}{2}(C_P+C_V)(Ti-T_f)$
(4) $(C_P-C_V)(T_i-T_f)$

33.

One mole of a perfect gas in a cylinder fitted with a piston has a pressure P, volume V and temperature 273 K. If the temperature is increased by 1 K keeping pressure constant, the increase in volume is
(1) $\frac{2V}{273}$
(2) $\frac{V}{91}$
(3) $\frac{V}{273}$
(4) V

34.

A monoatomic gas is supplied with the heat \(Q\) very slowly, keeping the pressure constant. The work done by the gas will be:
1.\({2 \over 3}Q\)
2.\({3 \over 5}Q\)
3.\({2 \over 5}Q\)
4.\({1 \over 5}Q\)

35.

In pressure-volume diagram given below, the isochoric, isothermal, and isobaric parts respectively are -

(1) BA, AD, DC
(2) DC, CB, DA
(3) AB, BC, CD
(4) CD, DA, AB

Physics - Section B

36.

A thermodynamic system is taken from state A to B along ACB and is brought back to A along BDA as shown in the PV diagram. The net work done during the complete cycle is given by the area
(1) P₁ACBP₂P₁
(2) ACBB'A'A
(3) ACBDA
(4) ADBB'A'A

37.

A metre stick is swinging in vertical plane about a horizontal axis passing through its one end , undergoes small oscillation of frequency f₀. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become -

1.${\mathrm{f}}_0$
2.$\sqrt{2}{\mathrm{f}}_0$
3.$2{\mathrm{f}}_0$
4.$2\sqrt{2}{\mathrm{f}}_0$

38.

A travelling wave in a stretched string is described by the equation$\mathrm{y}=\mathrm{Asin}\left(\mathrm{kx}-\mathrm{\omega t}\right)$. The maximum particle velocity is:
1.$\mathrm{A\omega }$
2.$\mathrm{\omega }/\mathrm{k}$
3.$\mathrm{d\omega }/\mathrm{dk}$
4. x/t

39.

When \(x\) amount of heat is given to a gas atconstant pressure, it performs\(\frac{x}{3}\)amount of work. The average number of degrees offreedom per molecule of the gas is:
1. \(3\)
2. \(4\)
3. \(5\)
4. \(6\)

40.

The amplitude and the time period in an S.H.M. are 0.5 cm and 0.4 sec respectively. If the initial phase is$\mathrm{\pi }/2$ radian, then the equation of S.H.M. will be:
1.$\mathrm{y}=0.5\sin 5\mathrm{\pi t}$
2.$\mathrm{y}=0.5\sin 4\mathrm{\pi t}$
3.$\mathrm{y}=0.5\sin 2.5\mathrm{\pi t}$
4.$\mathrm{y}=0.5\cos 5\mathrm{\pi t}$

41.

An ideal gas going through the reversible cycle$\mathrm{a}\to \mathrm{b}\to \mathrm{c}\to \mathrm{d}$,has the V-T diagram as shown below in the figure. Process$\mathrm{d}\to \mathrm{a}\mathrm{and}\mathrm{b}\to \mathrm{c}$are adiabatic.

The corresponding P-V diagram for the process is (all figures are schematic and not drawn to scale):
1.
2.
3.
4.

42.

A particle is executing SHM with an amplitude of 4 cm. At the mean position, velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is
1.$\sqrt{3}$cm
2.$\sqrt{5}$cm
3. 2$\sqrt{3}$cm
4. 2$\sqrt{5}$cm

43.

In a stationary lift, a spring-block system oscillateswith a frequency \(f.\) When the lift accelerates, the frequency becomes \(f'\). Then:

44.

A simple pendulum with a metallic bob has a timeperiod T. The bob is now immersed in a nonviscous liquid and the time period is found to be $\sqrt{5}$T. The ratio of the density of the metal to that of liquid is
1. 1/4
2. 4/3
3. 5/4
4. 7/3

45.

A particle is moving along the x-axis. The speed ofparticle v varies with position x as $\frac{{\mathrm{v}}^2}{144}+\frac{{\mathrm{x}}^2}{9}=1$. The time period of S.H.M is
1.$\mathrm{\pi }\mathrm{unit}$
2.$\frac{3\mathrm{\pi }}{2}\mathrm{unit}$
3.$\frac{\mathrm{\pi }}{2}\mathrm{unit}$
4.$\frac{\mathrm{\pi }}{4}\mathrm{unit}$

46.

A simple pendulum of length l and bob of mass mis executing S.H.M with amplitude A. The maximum tension in the string will be
1.$\mathrm{mg}\left(\frac{\mathrm{l}}{\mathrm{l}+\mathrm{A}}\right)$
2.$\mathrm{mg}\left(\frac{{\mathrm{l}}^2+{\mathrm{A}}^2}{{\mathrm{l}}^2}\right)$
3.$\mathrm{mg}\left(\frac{{\mathrm{l}}^2}{{\mathrm{l}}^2+{\mathrm{A}}^2}\right)$
4.$\mathrm{mg}\left(\frac{\mathrm{l}+\mathrm{A}}{\mathrm{l}}\right)$

47.

The position x (in centimeter) of a simple harmonic oscillator varies with time t (in second) as$x=2\cos \left(0.5\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}\right)$.The magnitude of the maximum acceleration of the particle in $\mathrm{cm}/{\mathrm{s}}^2$ is:
1.$\mathrm{\pi }$/2
2.$\mathrm{\pi }$/4
3.${\mathrm{\pi }}^2$/2
4.${\mathrm{\pi }}^2$/4

48.

A particle is executing S.H.M. such that itsacceleration 'a' is a function of displacement x as $\mathrm{a}=-\mathrm{\beta }\left(\mathrm{x}-6\right)$.The time period of the oscillation is
1.$\frac{\mathrm{\pi }}{\mathrm{\beta }}$
2.$\frac{\mathrm{\pi }}{2\mathrm{\beta }}$
3.$\frac{2\mathrm{\pi }}{\sqrt{2}\mathrm{\beta }}$
4.$\frac{2\mathrm{\pi }}{\sqrt{\mathrm{\beta }}}$

49.

A particle starts SHM from the mean position. Itsamplitude is A and time period is T. At the time when its speed is half of its maximum speed, its displacement is
1.$\frac{\mathrm{A}}{2}$
2.$\frac{\mathrm{A}}{\sqrt{2}}$
3.$\frac{\mathrm{A}\sqrt{3}}{2}$
4.$\frac{2\mathrm{A}}{\sqrt{3}}$

50.

Which of the following may represent the potentialenergy of a body in S.H.M.? (Symbols have usual meaning)
1.${\mathrm{m\omega }}^2{\mathrm{A}}^2$
2.$\frac{1}{2}{\mathrm{m\omega }}^2{\mathrm{X}}^2$
3.$\left(2{\mathrm{A}}^2+\frac{1}{{\mathrm{m\omega }}^2}\right)$
4. both (2) and (3)

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