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Physics
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In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the frequency.

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

In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the wave velocity.

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

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In the given progressive wave y = 5 sin (100 πt – 0.4 πx) where y and x are in m, t is in s. What is the particle velocity amplitude.. 

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

Given a + b + c + d = 0, state whether the following statement is correct or incorrect:

b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear.

[3] Motion in a Plane
Chapter: [3] Motion in a Plane
Concept: undefined >> undefined

Establish the following vector inequalities geometrically or otherwise:

  1. | a+b | ≤ |a| + |b|
  2. |a + b| ≥ | |a| - |b| |
  3. |a - b| ≤ |a| + |b|
  4. |a-b| ≥ | |a| - |b| |

When does the equality sign above apply?

[3] Motion in a Plane
Chapter: [3] Motion in a Plane
Concept: undefined >> undefined

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centers of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

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

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun = 2 x 1030 kg).

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

Give the magnitude and direction of the net force acting on a drop of rain falling down with a constant speed.

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

The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

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

If the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks?

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

Read each statement below carefully, and state, with reasons, if it is true or false;

 During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body

[6] System of Particles and Rotational Motion
Chapter: [6] System of Particles and Rotational Motion
Concept: undefined >> undefined

Read each statement below carefully, and state, with reasons, if it is true or false;

The instantaneous acceleration of the point of contact during rolling is zero.

[6] System of Particles and Rotational Motion
Chapter: [6] System of Particles and Rotational Motion
Concept: undefined >> undefined

A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain?

[8] Mechanical Properties of Solids
Chapter: [8] Mechanical Properties of Solids
Concept: undefined >> undefined

A vertical off-shore structure is built to withstand a maximum stress of 109 Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.

[9] Mechanical Properties of Fluids
Chapter: [9] Mechanical Properties of Fluids
Concept: undefined >> undefined

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? The surface tension of mercury at that temperature (20°C) is 4.65 × 10–1 N m–1. The atmospheric pressure is 1.01 × 105 Pa. Also give the excess pressure inside the drop

[9] Mechanical Properties of Fluids
Chapter: [9] Mechanical Properties of Fluids
Concept: undefined >> undefined

A tank with a square base of area 1.0 m2 is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm2. The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. compute the force necessary to keep the door close.

[9] Mechanical Properties of Fluids
Chapter: [9] Mechanical Properties of Fluids
Concept: undefined >> undefined

It is known that density ρ of air decreases with height as `0^(e^(y/y_0))` Where`rho_0` 1.25 kg m–3 is the density at sea level, and y0 is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also, assume that the value of gremains constant

[9] Mechanical Properties of Fluids
Chapter: [9] Mechanical Properties of Fluids
Concept: undefined >> undefined

Explain why Two bodies at different temperatures T1 and T2, if brought in thermal contact, do not necessarily settle to the mean temperature (T1 + T2)/2.

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

Explain why Air pressure in a car tyre increases during driving.

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

In changing the state of a gas adiabatically from an equilibrium state to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state to via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case? (Take 1 cal = 4.19 J)

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