Physics
2021 · Paper 1
Take it one question at a time. Try an answer, then check your understanding.
Complete GATE PH 2021 Paper 1 overview, original pages and practice · Timed previous-paper practice
Questions 40–42 of 65. Imported answers require review unless explicitly marked reviewed.
Question 30
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Consider a point charge
of mass
suspended by a mass, inextensible string of length
in free space (permittivity
) as shown in the figure. It is placed at a height
(
) over an infinitely large, grounded conducting plane. The gravitational potential energy is assumed to be zero at the position of the conducting plane and is positive above the plane. If
represents the angular position and
its corresponding canonical momentum, then the correct Hamiltonian of the system is 
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Consider two concentric conducting spherical shells as shown in the figure. The inner shell has a radius
and carries a charge +Q. The outer shell has a radius
and carries a charge
. The empty space between them is half-filled by a hemispherical shell of a dielectric having permittivity
. The remaining space between the shells is filled with air having the permittivity
. 
The electric field at a radial distance
from the center and between the shells (
) isYour answerChoose one option.
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For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respectively, choose the best suited interpretation.
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