Physics Test 243

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Physics Test 243

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Question 1
4 / -1

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which ball can be moved?

A
14 m/s

B
3 m/s

C
3.92 m/s

D
5 m/s

Solution
Question 2
4 / -1

Two wires A and B are of the same materials. Their lengths are in the ratio 1 : 2 and the diameters are in the ratio 2 : 1, When stretched by force F_A and F_B respectively they get equal increase in their lengths. Then the ratio should be:

A
1 : 2

B
1 : 1

C
2 : 1

D
8 : 1

Solution
Question 3
4 / -1

In a capillary tube of radius 'R', a straight thin metal wire of radius 'r' (R > r) is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is [T = surface tension of water, ρ = density of water, g = gravitational acceleration]

A

B

C

D

Solution
Question 4
4 / -1

A circuit connected to an ac source of emf e = e₀sin(100t) with t in seconds, gives a phase difference of between the emf e and current i. Which of the following circuits will exhibit this ?

A

B

C

D

Solution
Question 5
4 / -1

A mass of 100g strikes the wall with speed 5m/s at an angle as shown in figure and it rebounds with the same speed. If the contact time is 2 × 10⁻³sec, what is the force applied on the mass by the wall.

A
250 √3 to right

B
250 N to right

C

D
250N to left
Solution
Concept:

Force and Change in Momentum:
- The force is given as the rate of change of momentum.
- Momentum is a vector quantity and can have positive/negative directions.
The negative sign indicates the force acts in the opposite direction.
Question 6
4 / -1

A wire of length ‘l’ and resistance 100 Ω is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:

A
26 Ω

B
52 Ω

C
55 Ω

D
60 Ω

Solution

Calculation:

Wire resistance = 100 Ω

Divide into 10 equal parts

so each part resistance r = (100 / 10 )+ 10 Ω

R_eq= 5× 10 +(10/5)

R_eq = 52

The correct answer is option 2.
Question 7
4 / -1

Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would

A
Increase by 4 times

B
Increase by 2 times

C
Decrease by 2 times

D
Decrease by 4 times
Solution
Concept:
- The wavelength of the electron due to its motion is called the de-Broglie wavelength of the electron.
- The bundle of light rays is called a photon.
- The de-Broglie wavelength of an electron (λ_e) is given by:
Where h = Plancks constant, m = mass of the particle, V = Velocity
- The de Broglie wave equation explains the dual nature of matter as it connects the wave characteristics, λ to particle characteristics P.
- The wavelength of an electron accelerated through a potential V is given by
When the voltage was increased from 25Kv to 100 Kv then the de-Broglie wavelength associated with the electrons would decrease by 2 times. Therefore option 3 is correct.
Question 8
4 / -1

A metal target with atomic number Z = 46 is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio r of the wavelengths of the K_α-line and the cut-off is found to be r = 2. If the same electron beam bombards another metal target with Z = 41, the value of r will be

A
2.53

B
1.27

C
2.24

D
1.58

Solution
Question 9
4 / -1

If two traveling waves, given by

𝑦₁ = 𝐴₀sin(𝑘𝑥 − 𝜔𝑡) and 𝑦₂ = 𝐴₀sin(α𝑘𝑥 − β𝜔𝑡)

are superposed, which of the following statements is correct?

A
For α = β = 1, the resultant wave is a standing wave

B
For α = β = −1, the resultant wave is a standing wave

C
For α = β = 2, the carrier frequency of the resultant wave is

D
For α = β = 2, the carrier frequency of the resultant wave is 3𝜔

Solution

Concept :
This problem deals with wave interference and the formation of standing waves . When two traveling waves moving in opposite directions interfere, they can form a standing wave if the conditions are right. A standing wave occurs when the superposition of two waves results in a pattern of nodes and antinodes. The frequency of the resulting standing wave depends on the wave number k, angular frequency , and the specific parameters of the waves involved in the interference.
Question 10
4 / -1

A transverse wave is represented by the equation For what value of λ the maximum particle velocity is equal to two times the wave velocity

A

B
πy₀

C
2πy₀

D

Solution

Concept:

The maximum particle velocity refers to the highest speed at which the individual particles of the medium oscillate as the wave passes through them.

The wave velocity is the speed at which the wave propagates through the medium.

Calculation:

The particle velocity is obtained by differentiating the wave equation with respect to time,