Physics: Topic-wise Test- 2 - NEET MCQ

The two masses are at a distance of “a” and “a/2” so,

Let the acceleration due to gravity at that height is g′.

The acceleration due to gravity at some height (g′ ) = 1% of the acceleration due to gravity(g ) at the surface of the earth.

According to question

g′ = 1% of g

g′ = 1 / 100 × g

g′ = g / 100

The acceleration due to gravity at a height h above the surface of the earth is;

g′ = g (R / R+h)² , Where R is the radius of the earth.

Thus,

g / 100 = g(R / R+h)²

1 / 100 = (R / R+h)²

Taking square root on both sides we get,

1 / 10 = (R / R+h)

R+h = 10R

h = 9R

W = increase in potential energy of system

=U_f - U_i

=m (V_f - V_i)

(V = gravitational potential)

Note: Even if mass is nonuniformly distributed potential at centre would be -GM/R

The center of mass (CM) for two point masses can be calculated using the formula:

Here, let m₁ = 4m (mass at position 0) and m₂ = m (mass at position d).

Now, we can find the distances of each mass from the center of mass:

For circular motion, the centripetal force acting on each mass is given by:

F_c = m⋅r⋅ω²

Where r is the distance from the center of mass and ω is the angular velocity.

For mass 4m:
F_c,4m = 4m⋅d / 5⋅ω²

For mass m:
F_c,m = m⋅4d / 5⋅ω²

Since both masses are in circular motion due to their mutual gravitational attraction, we can set the centripetal forces equal to each other:

4m⋅d / 5⋅ω² = m⋅4d / 5⋅ω²

The kinetic energy (KE) for each mass in rotational motion is given by:

K.E. = 1 / 2Iω²

Where I is the moment of inertia. The moment of inertia for point masses is given by I = m⋅r².

For mass 4m:

For mass m:

Now, we can find the ratio of the kinetic energies:

Thus, the ratio of the kinetic energies of the two masses is:

Ratio of Kinetic Energies = 1 : 4

The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely provides the centripetal force needed for the rotation. Let M be the mass of the planet R its radius and m the mass of a particle on its surface. Then

Angular momentum of planet about the sun is constant.

i.e. mυr sin θ = constant

At position P and Q, θ = 90⁰ and m = mass of planet = constant

∴ υr = constant

We know that the efficiency of refrigeration for a refrigerator is T₂ / T₁ + T₂
Where T₁ is source temperature and T₂ is sink temperature
For refrigerator X we have T₁ = 298K and T₂ = 268K
Hence the efficiency of refrigeration = 268 / 298 - 268
= 268 / 30
= 8.93
For refrigerator Y we have T₁ = 293K and T₂ = 253K
Hence the efficiency of refrigeration = 253 / 293 - 253
= 253 / 40
= 6.35

It works on the principle that no machine is 100% efficient. For instance if taking an ideal machine into consideration, work can be completely converted to heat. Now if the conditions are reversed, all heat cannot be converted to equal amount of work until and unless backed up by an external force.

A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it’s the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both).

If first law efficiency is close to unity, the all the energy carried in by heat transfer is used and no heat is lost to the surroundings.

The second law of thermodynamics gives a fundamental limitation to the efficiency of a heat engine and the coefficient of performance of a refrigerator. It says that the efficiency of a heat engine can never be unity or 100%, this implies that the heat released to the cold reservoir can never be made zero.
For a refrigerator the second law says that the coefficient through performance can never be infinite, this implies that the external work can never be zero.

If you leave the door open, heat is merely recycled from the room into the refrigerator, then back into the room. A net room temperature increase would result from the heat of the motor that would be constantly running to move energy around in a circle.

As change of state depends on both temperature and pressure, so, either method A or C can be used. We can understand this by ideal gas equation PV = nRT

No, heat is not transferred as the flask is insulated from the surroundings ∴dQ=0

Wall that permits *heat" to flow through them,such as engine block is called diathermic wall.
wall Perfectly insulating ball that doesn't allow the flow heat to them are called adiabatic walls.

On heating, the copper strip will suffer greater elongation and hence the bimetal strip will bend with the steel strip on the concave side. 

[Bimetal strips are widely used in thermal switching applications such as automatic electric iron].

The rate of heat transfer is directly proportional to the bisectional surface area of the solid and inversely proportional to its parallel length. 
That is heat conduction rate say H ∝ r²
∝ 1/L
I.e ∝ r²/L
Hence the conduction would be
maximum in case in which  r²/L ratio is largest.

The Celsius and Fahrenheit are two important temperature scales. The Fahrenheit scale is used primarily in the United States, while Celsius is used throughout the world. The two scales have different zero points and the Celsius degree is bigger than the Fahrenheit one. There is one point on the Fahrenheit and Celsius scales where the temperatures in degrees are equal. This is -40 degree C and -40 degree F.

When heated the length between adjacent markings increases. Hence the actual length will be less than
30 cm.

Cubical expansion means there is expansion is length (a1), breadth (a2) and height (a3). Therefore the net coefficient of cubical expansion is α1 + α2 + α3.

To find the shear strain produced in the rubber cube, we use the following steps:

• The shear modulus (η) is given as 2 x 10⁶ N/m².
• The side of the cube is 10 cm, which is 0.1 m.
• The tangential force applied is 1800 N.
• The area of the side where the force is applied is:
  Area = Side x Side = 0.1 m x 0.1 m = 0.01 m².
• Calculate the shear stress (force per area):
  Shear Stress = Force / Area = 1800 N / 0.01 m² = 180,000 N/m².
• The shear strain is the ratio of shear stress to shear modulus:
  Shear Strain = Shear Stress / η = 180,000 N/m² / 2 x 10⁶ N/m² = 0.09.

Thus, the shear strain produced is 0.09.

Young's Modulus of elasticity =stress/strain
Y= [F/a/△l/l] ​ or Y= [Fl​/a△l]
or △l= [Fl/aY] ​= Fl​/ πr²Y
In the given problem, △l∝ l​/ r²
When both l and r are doubled, △l is halved.

We know that magnitude of bulk modulus
K=[P/(dV/V)]
Now, percentage change in volume is. 10^-3 %
Therefore, (dV/V)x100=10^-3
So, dV/V=10^-5
Hence, k is,
K=40atm/10^-5=40x1.01x10⁵ /10^-5 =4.04x10¹¹ N/m²