Physics Test 217

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Physics Test 217

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Question 1
4 / -1

Two cylindrical rods of uniform cross-sectional area A and 2A, having free electrons per unit volume 2n and n respectively are joined in series. A constant current I flows through them in steady state. The ratio of the drift velocity of free electrons in the left rod to that of the right rod is

A
1/2

B
1

C
2

D
4

Solution

Since current, I = ne Av_d through both rods is the same.

⇒ (2n)eAv_L= ne(2A)v_R

⇒ v_L/v_R = 1
Question 2
4 / -1

Water is filled up to a height h in a cylindrical vessel. It takes time t to completely drain the vessel by means of a small hole at the bottom. If water is filled up to a height 4h then the time it takes to completely drain the vessel is

A
t

B
4t

C
2t

D
t/4

Solution
Question 3
4 / -1

A refrigerator is to maintain the eatables, kept inside it, at 9°C. The coefficient of performance of the refrigerator, if the room temperature is 36°C, is

A
10.45

B
4

C
3

D
11.45

Solution

Here, T₁ = 36℃ = 36 + 273 = 309 K

T₂ = 9℃ = 9 + 273 = 282 K

The coefficient of performance of a refrigerator is given by
Question 4
4 / -1

An elevator is going upward with an acceleration a = g/4 and a ball is released from rest relative to the elevator at a distance h₁ above the floor. The speed of the elevator at the time of ball release is v₀. Then the bounce height h₂ of the ball with respect to the elevator is (the coefficient of restitution for the impact is e)

A
eh₁

B
e²h₁

C
e³h₁

D
None of these

Solution
Question 5
4 / -1

The magnetic flux through a circuit of resistance R changes by an amount Δϕ in a time Δt. The total magnitude of electric charge Q, that passes through any point in the circuit during this time is

A

B

C

D

Solution
Question 6
4 / -1

To get maximum current through a resistance of 2.5 Ω, one can use mm rows of cells, each row having n cells. The internal resistance of each cell is 0.5 Ω. What are the values of n & m, if the total number of cells is 45?.

A
3, 15

B
5, 9

C
9, 5

D
15, 3

Solution

For maximum current :

Net external resistance = net internal resistance.
Question 7
4 / -1

An iron wire AB of length 3 m at 0°C is stretched between the opposite walls of a brass casing at 0°C0°C as shown in the figure below. The diameter of the wire is m0.6 mm. What extra tension will be set up in the wire when the temperature of the system is raised to 40°C?

Given α_brass= 18 × 10⁻⁶ K⁻¹, α_iron= 12 × 10⁻⁶ K⁻¹, Y_iron= 21 × 10¹⁰ N m⁻²

A
14.2 N

B
13.8 N

C
21.3 N

D
28.4 N

Solution

Increase in length of the iron wire = LαΔt = L × 12 × 10⁻⁶× 40 = 48L × 10⁻⁵ m

Increase in length of the brass tube = LαΔt = L × 18 × 10⁻⁶× 40 = 72L × 10⁻⁵ m

Since the increase in length of the brass tube is greater than that of the iron wire, the latter will be tightened. Let T be the tension in the wire. Then,

T = 21 × 10¹⁰× 24 × 10⁻⁵× 9π × 10⁻⁸= 14.2 N
Question 8
4 / -1

Four metal plates numbered 1, 2, 3 and 4 are arranged, as shown in figure. The area of each plate is A and the separation between them is d. The capacitance of the arrangement is

A

B

C

D

Solution

Plate 1 is connected to plate 3 and plate 2 is connected to plate 4. Thus, there are three capacitors in parallel, each of capacitance
Question 9
4 / -1

The angular width of the central maximum in the Fraunhofer's diffraction pattern is measured. The slit is illuminated by the light of wavelength 6000 Å. If the slit is illuminated by the light of another wavelength, angular width decreases by 30% . The wavelength of light used is

A
3500 Å

B
4200 Å

C
4700 Å

D
6000 Å

Solution

For the first diffraction minimum, dsinθ=λ

And if the angle is small, sinθ = θ

dθ = λ

i.e., Half angular width, θ = λ/d

Full angular width w = 2θ = 2λ/d
Question 10
4 / -1

What will be the displacement equation of the simple harmonic motion obtained by combining the motions?

(Note: ϕ is an acute angle)

A
x = 10.25sin(ωt + ϕ)

B
x = 10.25 sin(ωt − ϕ)

C
x = 11.25 sin(ωt + ϕ)

D
x = 11.25 sin(ωt − ϕ)

Solution

The resultant equation is

x = A sin(ωt + ϕ)

∑A_x= 2 + 4cos30° + 6 cos 60° = 8.46

Thus, the displacement equation of combined motion is

x = 11.25sin(ωt + ϕ)

Where, ϕ = 40.4°