Physics Test 296

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Physics Test 296

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Weekly Quiz Competition

Question 1
4 / -1

What is the De-Broglie wavelength of an electron orbiting in the n = 2 state of a hydrogen atom?

(Given: Bohr radius = 0.052 nm)

A
0.067 nm

B
0.67 nm

C
1.67 nm

D
2.67 nm

Solution

Correct option is: (2) 0.67 nm

Given n = 2, Z = 1

2πr = nλ

2π × (0.052 × n² / Z) = nλ

On solving, λ = 0.67 nm
Question 2
4 / -1

The headlight of a train of length 200 m is switched on when it starts from rest with an acceleration of 0.5 ms^–2. After 20 s, its tail-light is switched on. An observer in a frame moving with a constant velocity parallel to the railway track observes that the two events occur at the same place. The velocity of this frame is

A
5 ms^–1 in a direction opposite to the train’s motion

B
10 ms^–1 in a direction opposite to the train’s motion

C
5 ms^–1in the same direction as the train’s motion

D
10 ms^–1 in the same direction as the train’s motion

Solution

Distance traveled by the train in 20 seconds:

Position of the Train

The distance traveled by the train after 20 seconds:

d = 100m

The position of the tail light when it is switched on:

x₂= −100m

Condition in the Moving Frame

The events occur at the same place in the moving frame, so:

x′₁= x′₂⇒ 0 = −100 − 20v

The velocity of the moving frame is:

v = −5 m/s, the negative sign indicates direction opposite to the train’s motion.

∴ The correct option is 1
Question 3
4 / -1

The density inside a solid sphere of radius a is given by ρ = ρ₀ (a/r), where ρ₀ is the density at the surface and r denotes the distance from the centre. The gravitational field due to this sphere at a distance 3a from its centre is

A

B

C

D

Solution

Gravitational Field at a Distance 3a

Since the distance 3a is outside the sphere, we can treat the total mass M as if it is concentrated at the center.

The gravitational field at a distance r = 3a is given by Newton’s law of gravitation,
Question 4
4 / -1

A tuning fork with a frequency of 800 Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm, and 52.75 cm. The speed of sound in air is,

A
344 m/s

B
172 m/s

C
500 m/s

D
156 m/s

Solution
Question 5
4 / -1

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?

A

B

C

D

Solution

Charge Q with a surface charge density σ on a spherical body of radius R is given as:

Q = σ×4πR² -----(1)

Potential of a sphere with charge Q and radius R is given as:

Given:

Radius of 1st sphere = R

Radius of 2nd sphere = 2R

Surface charge density on both 1st and 2nd sphere = σ

Now, suppose initial charge on 1st sphere is Q₁ and that on 2nd sphere is Q₂.

Using equation (1) we have,

Q₁ = σ×4πR² &

Q₂ = σ×4π(2R)² = 4Q₁ -----(3)

After separating shperes when brought in contact both have same potential.
Question 6
4 / -1

The output (Y) of the given logic implementation is similar to the output of an/a _______ gate.

A
AND

B
NAND

C
OR

D
NOR

Solution
Question 7
4 / -1

From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

A

B

C

D

Solution

When the volume of the cube is maximum, the longest diagonal of the cube is equal to the diameter of the sphere.

Given: FG = GC = L

Then, FC = √(FG² + GC²) = √(L² + L²) = √2 × L

FD = √(FC² + CD²) = √((√2 × L)² + L²) = √3 × L

So, √3 × L = 2R ⇒ L = 2R / √3

Since mass ∝ volume, we have:

Mass of cube / Mass of sphere = Volume of cube / Volume of sphere

⇒ M_C = (V_C / V_S) × M_S

⇒ M_C = ((2R / √3)³) / ((4/3) × π × R³) × M

⇒ M_C = (2M) / (√3 × π)

Moment of inertia of the cube about an axis through its center and perpendicular to one of its faces is:

I = (1/6) × M × L²

⇒ I = (1/6) × (2M / √3π) × (2R / √3)²

⇒ I = (4M × R²) / (9√3π)
Question 8
4 / -1

In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1 m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1 g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment?

A
1.4%

B
0.9%

C
0.14%

D
9%

Solution
Question 9
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

Given: ρ_water = 1000 kg/m³, h_water = 15 cm and h_oil = 20 cm

As in the given question, the pressure of the oil = the pressure of the water and it is written as;
Question 10
4 / -1

A deep rectangular pond of surface area A, containing water (density = ρ, specific heat capacity = s), is located in a region where the outside air temperature is at a steady value of −26°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant, would be given by

A
26K/(ρxL)

B
26K/ρx(L + 4s)

C
26K/ρx(L − 4s)

D
26K/(ρx²L)

Solution