Physics Test 212

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Physics Test 212

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Question 1
4 / -1

If force F is related with distance x and time t as F = A√x + Bt², the dimensions of A/B is

A
M⁰L^−1/2T

B
ML^−1/2T⁻²

C
M⁰L^−1/2T²

D
M⁰ LT^–2

Solution

All terms of an equation must have same dimensions
Question 2
4 / -1

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration aa directed horizontally as shown in the figure. Another end of the string is pulled with constant acceleration a vertically. The tension in the string is equal to :

A

B

C

D
m (g + a)

Solution
Question 3
4 / -1

A disc of mass M and radius R is rolling with angular speed ω on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

A
(1/2) M R²ω

B
M R²ω

C
(3/2) M R²ω

D
2M R²ω

Solution

Angular momentum about O = Angular momentum about CM + Angular momentum of CM about origin

L₀ = I_ω + MR_v
Question 4
4 / -1

The magnitude of the maximum acceleration is π times that of the maximum velocity of a simple harmonic oscillator. The time period of the oscillator in seconds is

A
4

B
2

C
1

D
0.5

Solution

Maximum acceleration = Maximum velocity × π

I.e., ω²A = πωA

where A is amplitude and ω is angular velocity.

⇒ ω = π

⇒ 2π/T = π

⇒ T = 2 s
Question 5
4 / -1

An object of specific gravity ρ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is 300 Hz. The object is immersed in water, so that one half of its volume is submerged. The new fundamental frequency (in Hz) is

A

B

C

D

Solution

The diagrammatic representation of the given problem is shown in figure. The expression of fundamental frequency is
Question 6
4 / -1

One mole of ideal gas goes through process then change in temperature of the gas when volume changes from V = 1 m³ to 2 m³ is:

A

B

C

D
2 K

Solution
Question 7
4 / -1

A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity as shown, the force on the charge is

A
Along OY

B
Opposite to OY

C
Along OX

D
Opposite to OX

Solution
Question 8
4 / -1

The ratio of the volume occupied by an atom to the volume of the nucleus is

A
10⁵ : 1

B
10²⁰ : 1

C
10¹⁵ : 1

D
1 : 10¹⁵

Solution

The radius of an atom = r_A ≈ 10⁻¹⁰ m

The radius of the nucleus = r_N ≈ 10⁻¹⁵ m

So, the ratio of their volumes is
Question 9
4 / -1

Energy from the sun falls on the earth at a rate of 1353 W/m², which is known as solar constant, i.e., the power incident per unit area per second at the top of atmosphere. Find the r.m.s values of the electric and magnetic fields in the sunlight reaching the top of the atmosphere.

A
714.0 V/m, 2.38 × 10^–6 T

B
7.14 V/m, 2.38 × 10^-8 T

C
71.4 V/m, 2.38 × 10^–7 T

D
None of these

Solution
Question 10
4 / -1

The effect on the interference fringes if the monochromatic source is replaced by a source of white light would be:

A
Interference pattern disappears

B
Fringe separation remains fixed

C
Fringe closest to the central fringe is red.

D
Fringe separation increases

Solution

The interference patterns due to different component colours of white light overlap (incoherently). The central bright fringes for different colours are at same position. Therefore, the central fringe is white.

For a point P for which:

S₂P - S₁P = λ_b/2

λ_b ≈ 4000 Å represents the wavelength of blue colour, the blue colour will be absent and the fringe will appear red in colour. Slightly farther away where,

S₂Q - S₁Q = λ_b = λ_r/2

Where λ_r ≈ 8000 Å represents the wavelength of red colour, the fringe will be predominantly blue.