Physics Test 246

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Physics Test 246

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Question 1
4 / -1

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to of its initial value?

A
20 minutes

B
40 minutes

C
60 minutes

D
80 minutes
Solution
Concept:

Radioactive Decay:
- Radioactive decay is a process by which an unstable atomic nucleus loses energy by radiation.
- The activity of a radioactive substance is the number of decays per unit time.
- The half-life (T_1/2) is the time required for half of the radioactive nuclei in a sample to decay.
- Half-life (T_1/2): The time required for a quantity to reduce to half its initial value. SI unit: seconds (s).
∴ The activity of the substance drops to 1/16 of its initial value in 80 minutes.
Question 2
4 / -1

In a u-tube as shown in the fig. water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is [take ρ_water = 1000 kg/m³]

A
1000 kg/m³

B
1333 kg/m³

C
1200 kg/m³

D
750 kg/m³

Solution

CONCEPT:

The pressure of the static fluid is defined as the product of the depth of the fluid, the density of the fluid, and acceleration due to gravity we have;
Question 3
4 / -1

Two small spherical metal balls, having equal masses, are made from materials of densities ρ₁ and ρ₂ (ρ₁ = 8ρ₂) and have radii of 1 mm and 2 mm, respectively, They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1 ρ₂. The ratio of their terminal velocities would be,

A
39/72

B

C
79/72

D
19/36
Solution
CONCEPT:

Terminal Velocity:
- It is the maximum constant velocity acquired by the body while falling freely in a viscous medium.
- When a body falls freely through a viscous medium, three forces act on it.
Where, v = Terminal velocity,

r = Radius of the spherical body,

g = Acceleration due to gravity (constant for big and smaller spheres),

ρ = Density of the body (constant for big and smaller spheres),

σ = Density of the medium through which the body is falling (constant for big and smaller spheres),

η = Coefficient of the viscosity of the medium through which the body is falling (constant for big and smaller spheres)
Question 4
4 / -1

Two identical capacitors C₁ and C₂ of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C₁ using battery of emf V volt. Now disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy ?

A
50%

B
25%

C
75%

D
0%

Solution

and when we connected the poles b and c we see that capacitors C₁,C₂ are in series, therefore the capacitance is written as;
Question 5
4 / -1

Choose the correct answer from the options given below:

A
(a) - (iv), (b) - (ii), (c) - (i), (d) - (iii)

B
(a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)

C
(a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)

D
(a) - (ii), (b) - (iv), (c) - (iii), (d) - (i)

Solution

Concept:

(a) gravitational constant is = G = Fr²/Mm

we know F = GMm/r² => G = Fr²/Mm where F = ma = M¹L¹T^-2

so G = M^-1L³T^-2 so (a) matches with (ii)

(b) Gravitational potential energy = mass × altitude × acceleration due to gravity

dimensional formula of mass = [M¹ L⁰ T⁰]   and dimensional formula of altitude = [M⁰ L¹ T⁰]

and acceleration due to gravity (g) = [M⁰ L¹ T^-2]

then dimensions of Gravitational potential energy = [M¹ L² T^-2] so that it matches with (iv).

(c) gravitational potential (V) = work done/ mass

dimensional formula of work done = Force × distance = [M¹ L² T^-2]

then dimensions of Gravitational potential = [M⁰ L² T^-2] so that it matches with (i).

(d)  Gravitational Intensity (Eg) = [- GM/r²]

from above gravitational constant has a dimensional formula as G = M^-1L³T^-2

then, dimensions of Gravitational intensity = [M⁰ L¹ T^-2] so that it matches with (iii).

Explanation:

As we have concluded in the concept section :

(a) matches with (ii)

(b) matches with (iv).

(c) matches with (i).

(d)matches with (iii).

Hence option 3) is correct.
Question 6
4 / -1

Given below are two statements :

Statement I :

Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (IdI) of a current carrying conductor only.

Statement II :

Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.

In light of above statements choose the most appropriate answer from the options given below:

A
Statement I is incorrect and Statement II is correct

B
Both Statement I and Statement II are correct

C
Both Statement I and Statement II are incorrect

D
Statement I is correct and Statement II is incorrect

Solution

CONCEPT:

Biot - Savart's law gives the equation of magnetic field produced by the current carrying segment and it is written as;

Here we have B as the magnetic field, I is the current, and r is the distance.

EXPLANATION:

Statement I - Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (IdI) of a current carrying conductor only which is written as;

Therefore this statement is true.

Statement II - In statement II is given that Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q. The Biot- Savart's law is the equation of the magnetic field produced by the current carrying conductor whereas in coulomb's law we find the force of attraction and repulsion between the two masses. Biot-Savart's law is not analogous to Coulomb's inverse square law of charge q.

Therefore, this statement is false.

Hence, option 4) is the correct answer.
Question 7
4 / -1

A

B

C

D

Solution
Question 8
4 / -1

For a radioactive material, half life is 10 minutes. If initially there are 600 number of nuclei, the time taken in minutes for the disintegration of 450 nuclei is

A
20

B
10

C
15

D
30
Solution
Concept:
- Radioactive substances are those which decay by itself by emitting radioactive rays that is alpha, beta and gamma rays.
- The duration of time in which the amount of radioactive substance reduces to half of its initial amount is known as half life.
- Formula of half life of a radioactive substance is
Question 9
4 / -1

A

B

C
λ₀

D
λ₀t

Solution

Concept:

de Broglie proposed that matter have dual character that is wave as well as particle similar to that of light.

The wavelength of wave associated with matter is calculated using the following formula
Question 10
4 / -1

When the light of frequency 2v₀ (where v₀ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v₁. When the frequency of the incident radiation is increased to 5v₀, the maximum velocity of electrons emitted from the same plate is v₂. The ratio of v₁ to v₂ is

A
1 ∶ 2

B
1 ∶ 4

C
2 ∶ 1

D
4 ∶ 1

Solution

Concept:

The phenomenon of ejection of electrons from metal surface when a light of frequency greater than the threshold frequency of it is incident on it is known as photoelectric effect.

Energy of incident photon is used to provide threshold energy to the electrons on the metal surface and the energy left is imparted to electron as its kinetic energy.

Equation connecting energy of incident photon and threshold energy and kinetic energy of ejected electron is