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Physics
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Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant):

1 + ωt + ω2t2

[13] Oscillations
Chapter: [13] Oscillations
Concept: undefined >> undefined

Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air is independent of pressure.

[14] Waves
Chapter: [14] Waves
Concept: undefined >> undefined

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Use the formula `v = sqrt((gamma P)/rho)` to explain why the speed of sound in air increases with temperature.

[14] Waves
Chapter: [14] Waves
Concept: undefined >> undefined

A bat emits an ultrasonic sound of frequency 1000 kHz in the air. If the sound meets a water surface, what is the wavelength of the the reflected sound? The speed of sound in air is 340 m s–1 and in water 1486 m s–1.

[14] Waves
Chapter: [14] Waves
Concept: undefined >> undefined

For the travelling harmonic wave

y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 4 m.

[14] Waves
Chapter: [14] Waves
Concept: undefined >> undefined

For the travelling harmonic wave

y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 0.5 m.

[14] Waves
Chapter: [14] Waves
Concept: undefined >> undefined

For the travelling harmonic wave

y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of `λ/2`.

[14] Waves
Chapter: [14] Waves
Concept: undefined >> undefined

For two vectors A and B, A + B = A − B is always true when

  1. |A| = |B| ≠ 0
  2. A ⊥ B
  3. |A| = |B| ≠ 0 and A and B are parallel or anti parallel
  4. When either |A| or |B| is zero
[3] Motion in a Plane
Chapter: [3] Motion in a Plane
Concept: undefined >> undefined

Given below in column I are the relations between vectors a, b and c and in column II are the orientations of a, b and c in the XY plane. Match the relation in column I to correct orientations in column II.

Column I   Column II
(a) a + b = c (i)
(b) a – c = b (ii)
(c) b – a = c (iii)
(d) a + b + c = 0 (iv)
[3] Motion in a Plane
Chapter: [3] Motion in a Plane
Concept: undefined >> undefined

A car of mass m starts from rest and acquires a velocity along east `v = vhati (v > 0)` in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is ______.

[4] Laws of Motion
Chapter: [4] Laws of Motion
Concept: undefined >> undefined

A body of mass 10 kg is acted upon by two perpendicular forces, 6 N and 8 N. The resultant acceleration of the body is ______.

  1. 1 m s–2 at an angle of tan−1 `(4/3)` w.r.t 6 N force.
  2. 0.2 m s–2 at an angle of tan−1 `(4/3)` w.r.t 6 N force.
  3. 1 m s–2 at an angle of tan−1 `(3/4)` w.r.t 8 N force.
  4. 0.2 m s–2 at an angle of tan−1 `(3/4)` w.r.t 8 N force.
[4] Laws of Motion
Chapter: [4] Laws of Motion
Concept: undefined >> undefined

A mass of 2 kg is suspended with thread AB (Figure). Thread CD of the same type is attached to the other end of 2 kg mass. Lower thread is pulled gradually, harder and harder in the downward directon so as to apply force on AB. Which of the threads will break and why?

[4] Laws of Motion
Chapter: [4] Laws of Motion
Concept: undefined >> undefined

In the above given problem if the lower thread is pulled with a jerk, what happens?

[4] Laws of Motion
Chapter: [4] Laws of Motion
Concept: undefined >> undefined

Block A of weight 100 N rests on a frictionless inclined plane of slope angle 30° (figure). A flexible cord attached to A passes over a frictonless pulley and is connected to block B of weight W. Find the weight W for which the system is in equilibrium.

[4] Laws of Motion
Chapter: [4] Laws of Motion
Concept: undefined >> undefined

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.

[7] Gravitation
Chapter: [7] Gravitation
Concept: undefined >> undefined

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.

  1. Change in internal energy is same in IV and III cases, but not in I and II.
  2. Change in internal energy is same in all the four cases.
  3. Work done is maximum in case I
  4. Work done is minimum in case II.
[11] Thermodynamics
Chapter: [11] Thermodynamics
Concept: undefined >> undefined

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?

[11] Thermodynamics
Chapter: [11] Thermodynamics
Concept: undefined >> undefined

Boyle’s law is applicable for an ______.

[12] Kinetic Theory
Chapter: [12] Kinetic Theory
Concept: undefined >> undefined

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) ______.

[12] Kinetic Theory
Chapter: [12] Kinetic Theory
Concept: undefined >> undefined

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?

[12] Kinetic Theory
Chapter: [12] Kinetic Theory
Concept: undefined >> undefined
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