Physics Test 228

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Physics Test 228

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Question 1
4 / -1

The terminal velocity (v_t) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

A
r^1/2

B
r

C
r²

D
r³

Solution

Explanation:

The terminal velocity of the spherical raindrop can be defined as,

where, r = radius of the sphere, η = viscosity of the medium, ρ₁ = density of sphere & ρ₂ = density of medium

From equation (1) we can say that-

Terminal velocity, v_t ∝ r².

Hence, Option 3) is the correct choice.
Question 2
4 / -1

Two systems A and B are in contact and are thermally insulated from their surroundings, but not from each other. It was noticed that the energy flows from system A to system B. This happened because

A
system A had more mass than system B

B
system A had more volume than system B

C
system A was at a higher temperature than system B

D
system A was kept on top of system B
Solution
The correct answer is option 3) i.e. system A was at a higher temperature than system B

CONCEPT:
- Heat: Heat is a form of energy and a measure of the internal energy contained in a system.
  
  It flows from a relatively high-temperature system to a relatively low-temperature system.
  
  The SI unit of heat is joule (J).
- Temperature: Temperature is the measure of heat energy contained in an object.
  
  It indicates the thermal state of a body.
  
  It determines the direction of the flow of heat when two bodies at different temperatures are placed in contact with each other.
  
  The SI unit of temperature is Kelvin (K).
EXPLANATION:
- Heat energy is capable of flowing from one object to another if there exists a temperature difference between the objects.
- Heat flows from an object at a higher temperature to an object at a lower temperature.
- Therefore, the energy flow from A to B indicates that the temperature of system A is higher than that of system B.
Question 3
4 / -1

On dipping a capillary in water the mass of the water that rises in it is 'm'. If another capillary of double the radius of the first is dipped into the water the mass of water rised will be

A
m/2

B
m

C
2m

D
4m

Solution

Concept:

The phenomenon of rising or falling of liquid level inside a capillary tube when it is dipped in the liquid is called capillary action.

The capillary action is due to surface tension.

Capillary action draws the ink to the tips of fountain pen nibs from a reservoir or cartridge within the pen.

This rise in water is equal to:

where T = surface tension of the fluid in contact with the fluid, θ = Angle of contact between the glass tube and the fluid, ρ = density of the fluid, and d = diameter of the glass tube.
Question 4
4 / -1

A heating element of mass 100 g and having specific heat of 1 J/(g°C) is exposed to surrounding air at 27°C. The element attains a steady state temperature of 127°C while absorbing 100 W of electric power. If the power is switched off, then approximate time taken by the element to cool down to 126°C will be (Neglect radiation)

A
0.1 s

B
1.0 s

C
5.0 s

D
10.0 s

Solution

Concept:

The measured difference between the total heat absorbed and the total heat released during a chemical reaction (performed at constant pressure) is called the heat of reaction or enthalpy change and is represented by ΔQ.
Question 5
4 / -1

A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 10%, then the rate of flow of liquid will change nearly by:

A
+10%

B
+46%

C
-10%

D
-40%
Solution
Concept:
- A constant pressure head cannot be maintained in a horizontal tube unless we consider the viscosity of the fluid.
- Viscosity is defined as a resistance of a fluid to a change in shape, or movement of neighboring portions relative to one another.
Calculation:

A constant pressure head cannot be maintained in a horizontal tube unless we consider the viscosity of the fluid.
Question 6
4 / -1

Find the force required at the plunger which has 3 cm diameter, and the diameter of the hydraulic press is 30 cm. It is used for lifting a weight of 30 kN.

A
200 N

B
150 N

C
100 N

D
300 N
Solution
Concept:

Pascal’s Law:
- It was given by Blaise pascal
- It is also known as the principle of transmission of fluid pressure
- It states that the pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.
- Alternate definition:- The pressure applied to any part of the enclosed liquid will be transmitted equally in all directions through the liquid.
Applications:
- The underlying principle of hydraulic jack and hydraulic press.
- Force amplification in the braking system of most motor vehicles.
- Used in artesian wells, water towers, and dams.
Calculation:

Given:

Diameter of plunger, d = 3 cm, Diameter of ram, D = 30 cm, Force required at the plunger = ?, Weight = 30 kN

According to pascals law,

Pressure applied at ram = Pressure exerted on the plunger
Question 7
4 / -1

A particle executes linear simple harmonic motion with frequency 0.40 Hz about the point x = 0. At t = 0, its displacement is 0.57 cm and velocity is zero. The displacement at time t is given by

A

B

C

D

Solution

CONCEPT:

Mathematically the displacement of a body undergoing simple harmonic motion can be written as

⇒ X = X_m cos ωt

Where X_m = maximum displacement of amplitude and ω = angular frequency

EXPLANATION:

Since the particle at t = 0 has a displacement 0.57 cm and since the velocity is zero there,

So, that must be the turning point and the amplitude = X_m = 0.57 cm

Now, the angular frequency ω = 2πf (f = linear frequency)

Given

f = 0.4 Hz

∴ ω = 2π(0.4) = 2π(2/5) = 4π/5

So, the displacement can be written as

→ X = X_mcos ωt = 0.57 cos (4π/5)t

Hence the correct answer is option 1.
Question 8
4 / -1

One gram of liquid water at 100°C is converted to steam at 100°C at standard atmospheric pressure (1.01 × 10⁵ Pa). The volume changes from 1 cm³ to 1671 cm³. The latent heat of vaporisation of water is 2260 J/g. The change in internal energy of the system, during this process, is close to

A
1.03 kJ

B
3.12 kJ

C
2.09 kJ

D
40.5 kJ

Solution

CONCEPT:

According to the first law of thermodynamics we have;
⇒ Q = ΔU + W
Here Q = amount of heat, ΔU = the change in internal energy, and W = work done.

EXPLANATION:

Given: mass, m = 1 g

Latent heat of vaporization, L = 2260 J/g

Pressure, P = 1.01 × 10⁵ Pa

The volume, (V₂ - V₁) = 1670 cm³

As we know that

Q = ΔU + W --- (1)

The work done, W = PdV

and heat Q = mL

Now, on putting the values in equation (1) we have;

mL = ΔU + P(V₂ - V₁)

Now, on putting all the given values in (2) we have;

1 x 2260 = ΔU + 1.01 × 10⁵(1670 x 10^-6)

⇒ ΔU= 2091.33 J ≈ 2.09 kJ

Hence the correct answer is option 3.
Question 9
4 / -1

The displacement of a particle in simple harmonic motion (SHM) is given by . What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?

A

B

C

D

Solution

Concept:

In general, the Simple Harmonic Motion is given by -

⇒ y = A sin (ω t + ϕ)

where A is constant, ω is Angular frequency and ϕ is the phase shift.

Solution:

The displacement of a particle in simple harmonic motion (SHM) is given by -
Question 10
4 / -1

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

A
λ

B
λ/2

C
2λ

D
4λ

Solution

EXPLANATION:

→The relation between frequency (f), wavelength (λ), and speed (v) of any wave is,

⇒ f = v/λ

→When sound waves are changing mediums wavelength and velocity changes.

But frequency always remains constant.

→If v₁ and v₂ be the velocities and λ₁ and λ₂ be the wavelengths of the soundwave in 1st and 2nd medium