GATE PH 2023 Paper 1 — page 14

Questions 40–42 of 65. Imported answers require review unless explicitly marked reviewed.

A rod

of proper length

lies along the

-axis and moves towards the positive

direction with speed

with respect to the ground (see figure), where

is the speed of light in vacuum. An observer on the ground measures the positions of

and

at different times

and

respectively in the ground frame, and finds the difference between them to be

. What is the value of

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A symmetric top has principal moments of inertia

about a set of principal axes 1, 2, 3, respectively, passing through its center of mass, where

is a positive constant. There is no force acting on the body and the angular speed of the body about the 3-axis is

rad/s. With what angular frequency in rad/s does the angular velocity vector

precess about the 3-axis?

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A particle of mass

is free to move on a frictionless horizontal two dimensional

plane, and is acted upon by a force

with

being a positive constant. If

and

are the generalised momenta corresponding to

and

respectively, then what is the value of

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2023 · Paper 1