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Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the mid point of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.
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Figure shows the P-V diagram of an ideal gas undergoing a change of state from A to B. Four different parts I, II, III and IV as shown in the figure may lead to the same change of state.

- Change in internal energy is same in IV and III cases, but not in I and II.
- Change in internal energy is same in all the four cases.
- Work done is maximum in case I
- Work done is minimum in case II.
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A person of mass 60 kg wants to lose 5kg by going up and down a 10 m high stairs. Assume he burns twice as much fat while going up than coming down. If 1 kg of fat is burnt on expending 7000 kilo calories, how many times must he go up and down to reduce his weight by 5 kg?
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Boyle’s law is applicable for an ______.
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1 mole of H2 gas is contained in a box of volume V = 1.00 m3 at T = 300K. The gas is heated to a temperature of T = 3000K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be (considering all gases to be ideal) ______.
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The volume of a given mass of a gas at 27°C, 1 atm is 100 cc. What will be its volume at 327°C?
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When air is pumped into a cycle tyre the volume and pressure of the air in the tyre both are increased. What about Boyle’s law in this case?
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A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be ______.
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Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is ______.

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The rotation of earth about its axis is ______.
- periodic motion.
- simple harmonic motion.
- periodic but not simple harmonic motion.
- non-periodic motion.
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A particle is in linear simple harmonic motion between two points A and B, 10 cm apart (Figure). Take the direction from A to B as the + ve direction and choose the correct statements.

- The sign of velocity, acceleration and force on the particle when it is 3 cm away from A going towards B are positive.
- The sign of velocity of the particle at C going towards O is negative.
- The sign of velocity, acceleration and force on the particle when it is 4 cm away from B going towards A are negative.
- The sign of acceleration and force on the particle when it is at point B is negative.
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In figure, what will be the sign of the velocity of the point P′, which is the projection of the velocity of the reference particle P . P is moving in a circle of radius R in anticlockwise direction.

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Sound waves of wavelength λ travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. Wavelength of sound waves in the second medium is ______.
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A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions ______.
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A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in ______.
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A transverse harmonic wave on a string is described by y(x, t) = 3.0 sin (36t + 0.018x + π/4) where x and y are in cm and t is in s. The positive direction of x is from left to right.
- The wave is travelling from right to left.
- The speed of the wave is 20 m/s.
- Frequency of the wave is 5.7 Hz.
- The least distance between two successive crests in the wave is 2.5 cm.
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Speed of sound waves in a fluid depends upon ______.
- directty on density of the medium.
- square of Bulk modulus of the medium.
- inversly on the square root of density.
- directly on the square root of bulk modulus of the medium.
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At what temperatures (in °C) will the speed of sound in air be 3 times its value at O°C?
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A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of 2.06 × 104N is applied?
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