Physics Test 255

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Physics Test 255

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Question 1
4 / -1

A long infinite current-carrying wire is bent in the shape as shown in the figure. The magnetic induction at point O is:

A

B

C

D

Solution

An infinite wire, carrying current, is bent in the following way.

Two semi-infinite parts and a bent finite part. We have to find the induced magnetic field at an external point o, at a distance R. The corresponding figure is shown below.

Magnetic field induced by a finite current-carrying conductor

The magnetic field at a distance R is given by:

B = (μ_₀ I / 4πR) (cos θ₁ - cos θ₂) ........(i)

where θ₁ and θ₂ are the angles made by the endpoints of the wire to the external point.

Using the right-hand thumb rule, we determine the direction of the magnetic field.

For the 1st semi-infinite part:

Given: θ₁ = 0 and θ₂ = 90° = π/2

Substituting these values in equation (i), we get:

B₁ = (μ_₀ I / 4πR)

For the bent portion:

Given: θ₁ = 45° and θ₂ = 135°

The magnetic field is calculated as:

B₂ = (μ_₀ I / 4πR) [ (1/√2) + (1/√2) ]

⇒ B₂ = (μ_₀ I / 2√2πR)

For the second semi-infinite part:

Given: θ₁ = π/2 and θ₂ = 0

The magnetic field is:

B₃ = (μ_₀ I / 4πR)

Total Magnetic Field:

Summing up the individual contributions, the total magnetic field at point O is:

B = B₁ + B₂ + B₃

⇒ B = (μ_₀ I / 2√2πR)
Question 2
4 / -1

A particle is projected with a velocity v so that its range on a horizontal plane is twice the greatest height attained If g is acceleration due to gravity, then its range is

A
4v²/5g

B
4g/5v²

C
4v³/5g²

D
4v/5g²

Solution
Question 3
4 / -1

A block of mass 30 kg is suspended by three strings as shown in figure. Find the tension in each string.

A
T_a = 450 N, T_b = 500 N,T_c = 300 N

B
T_a= 400 N, T_b= 500 N, T_c= 250 N

C
T_a= 400 N, T_b= 500 N,T_c= 300 N

D
T_a= 400 N, T_b= 550 N, T_c= 300 N

Solution

Method I: Considering equilibrium of each part of system The whole system is in equilibrium; therefore, for each part .

From the free-body diagram of block C, T_C= 300 N.
Question 4
4 / -1

A block of mass 1 kg is at rest on a horizontal table. The coefficient of static friction between the block and the table is 0.50. If g = 10 ms⁻², then the magnitude of a force acting upwads at an angle of 60^∘ from the horizontal that will just start the block moving is:

A
5 N

B
5.36 N

C
74.6 N

D
10 N

Solution

R + P sin 60 = Mg

R = Mg − P sin 60°

Frictional force

F = μR

= μ[Mg − Psin60^∘
Question 5
4 / -1

A disc of mass m and radius R placed on a smooth horizontal table as shown in figure. A light ideal string passes through the disc such that the one end of the string is attached to a small body of mass m and the other end is being pulled with a force F. The circumference of the disc is sufficiently rough so that the string does not slip over it. Find acceleration of the small body.

A
F/4m

B
F/m

C
F/2m

D
F/3m

Solution
Question 6
4 / -1

A block of wood floats in a liquid with four-fifths of its volume submerged. If the relative density of wood is 0.8, what is the the density of the liquid in units of kgm⁻³?

A
750

B
1000

C
1250

D
1500

Solution
Question 7
4 / -1

The potential energy of a particle of mass 1 kg.in motion along the x-axis is given by: U = 4(1 − cos2x), where x is in metres. The period of small oscillation (in seconds) is

A
2π

B
π

C
π/2

D
√2π

Solution
Question 8
4 / -1

A point mass is subjected to two simultaneous sinusoidal displacements in the x-directions: x₁(t) = A sin ωt and x₂(t) = A sin(ωt + 2π/3). Adding a third sinusoidal displacement x(t) = B sin(ωt + ϕ) brings the mass to a complete rest. The values of B and ϕ are respectively

A
√2A and 3π/4

B
A and 4π/3

C
√3A and 5π/6

D
A and π/3

Solution
Question 9
4 / -1

A positively charged ball hangs from a long silk thread. Electric field at a certain point (at the same horizontal level of the ball) due to this charge is E. Let us put a positive test charge q₀ at this point and measure F/q₀ on this charge. Then, E

A
> F/q₀

B
< F/q₀

C
= F/q₀

D
None of these

Solution
Question 10
4 / -1

A
4.4

B
8.2

C
24

D
28.4

Solution