Daily Olympiad: Physics - Modern Physics [20260512]

Challenge yourself with today's JEE Advanced practice! This test covers 'Modern Physics' for Physics (JEE Advanced - 12). Level: Expert | Duration: 60 mins.

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1. An electron is accelerated through a potential difference of 100 V and then subjected to a uniform magnetic field perpendicular to its motion. The radius of the circular path is found to be proportional to which of the following?

Solution
Correct: A
The radius of the path (r) for an electron in a magnetic field is given by $ r = \frac{mv}{qB} $. Since kinetic energy $ eV = \frac{1}{2}mv^2 $, velocity $ v $ is proportional to $ \sqrt{V} $. Substituting into the radius formula, $ r \propto \sqrt{V} $, making option A correct. Students must understand the relation between kinetic energy and velocity in electromagnetic interactions.

2. In the photoelectric effect experiment, if the frequency of incident light is increased beyond the threshold frequency while keeping its intensity constant, which of the following observations is/are correct?

Solution
Correct: B
The maximum kinetic energy ($ K.E = h(f - f_0) $) increases with frequency, but photoelectric current depends on intensity, not frequency. Since intensity is constant, the number of photons (and hence photoelectrons) remains the same, so the current stays constant. The correct answer is B. Students must distinguish between factors affecting kinetic energy and current.

3. A nucleus with mass number A splits into two daughter nuclei with mass numbers $ A_1 $ and $ A_2 $ ($ A_1 + A_2 = A $). Which condition ensures energy release in the fission process?

Solution
Correct: A
Energy is released when the binding energy per nucleon increases, i.e., daughter nuclei are more tightly bound than the parent. This is why fission of heavy nuclei (e.g., U-235) into smaller ones is energetically favorable. The correct answer is A. The student must connect binding energy trends and stability.

4. For a nucleus undergoing beta decay, its atomic number increases by 1. This implies the decay emits which of the following particles?

Solution
Correct: A
In beta-minus decay, a neutron converts into a proton, emitting an electron ($ \beta^- $) and an antineutrino. This increases the atomic number by 1, making option A correct. Students must recall beta decay mechanisms and the transformation of quarks within neutrons.

5. Two events occur at different points in inertial frame A and are simultaneous. In another inertial frame B moving at a constant speed relative to A, what can be said about their time ordering?

Solution
Correct: B
According to Einstein's relativity, simultaneity is not absolute. If two events are spatially separated in one frame, they cannot be simultaneous in all frames. The order can reverse depending on the direction of motion relative to event positions. Hence, option B is correct. This tests understanding of relativity of simultaneity.