Test: Classical Mechanics - 1 - Physics MCQ

# Test: Classical Mechanics - 1 - Physics MCQ

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## 20 Questions MCQ Test GATE Physics Mock Test Series 2025 - Test: Classical Mechanics - 1

Test: Classical Mechanics - 1 for Physics 2024 is part of GATE Physics Mock Test Series 2025 preparation. The Test: Classical Mechanics - 1 questions and answers have been prepared according to the Physics exam syllabus.The Test: Classical Mechanics - 1 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Classical Mechanics - 1 below.
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Test: Classical Mechanics - 1 - Question 1

### Consider a satellite in a circular orbit around the earth. Then properties of the satellite depend on the radius of the orbit r  as follows: speed  time period  angular momentum and kinetic energy

Detailed Solution for Test: Classical Mechanics - 1 - Question 1

For a satellite in a circular orbit

Test: Classical Mechanics - 1 - Question 2

### For streamline motion of an incompressible non-viscous fluid, is states by Bernoulli’s principle ____.

Detailed Solution for Test: Classical Mechanics - 1 - Question 2

Bernoulli's equation states that for an incompressible and inviscid fluid, the total mechanical energy of the fluid is constant. (An inviscid fluid is assumed to be an ideal fluid with no viscosity. )

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Test: Classical Mechanics - 1 - Question 3

### For the Lagrangian find equation of motion

Detailed Solution for Test: Classical Mechanics - 1 - Question 3

Explanation : L = (x'2+ x2y'2)/2 - kx2y2/2

d/dt(dL/dx) - dL/dx = 0

=> d/dt(x) - xy2 + kxy2 = 0

=> x'' = x(y')2 - kxy2

d/dt(dL/dy) - dL/dy = 0

d/dt(x2y) + kx2y = 0

=> x2y + 2xy + kx2y = 0

xy'' = -2x'y' - kxy

Test: Classical Mechanics - 1 - Question 4

A particle is placed in a region with the potential

Then,

Detailed Solution for Test: Classical Mechanics - 1 - Question 4

Test: Classical Mechanics - 1 - Question 5

A bullet is fired horizontally in the north direction with a speed u at θ latitude. It hits a target 1 meter away. Calculate the Coriolis acceleration.

Detailed Solution for Test: Classical Mechanics - 1 - Question 5

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Test: Classical Mechanics - 1 - Question 6

If a spring of spring constant k is stretched by x0, the work done is W0. Now, a second spring of spring constant 3k is stretched by x0/3. The work done is  The value of a is _____ (Correct upto two decimal place).

Detailed Solution for Test: Classical Mechanics - 1 - Question 6

For first spring,

∴

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Test: Classical Mechanics - 1 - Question 7

The moment of inertia of pairs of solid sphere each having mass m radius r kept in contact about a tangent passing through the point of contact is βmr2. The value of β is ______ . (Upto one decimal place)

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Test: Classical Mechanics - 1 - Question 8

The moment of inertia tensor of a rigid body is given by

Moment of inertia about an axis  is _______.

Detailed Solution for Test: Classical Mechanics - 1 - Question 8

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Test: Classical Mechanics - 1 - Question 9

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. The work required to pull the hanging part on the table is  The value of α is _________

Detailed Solution for Test: Classical Mechanics - 1 - Question 9

Test: Classical Mechanics - 1 - Question 10

The Hamiltonian of a system is given by

It describes the motion of

Detailed Solution for Test: Classical Mechanics - 1 - Question 10

Equations of motion are

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Test: Classical Mechanics - 1 - Question 11

The muon is an unstable particle that spontaneously decay into an electron and two neutrinos if the number of muons at t = 0 is N0 is the mean life time of muon. Suppose muons move at speed 0.95c, the number of muons remain after travelling a distance of 3.0 km is _______ (in terms of N0) (upto three decimal places)

Detailed Solution for Test: Classical Mechanics - 1 - Question 11

S frome attached to the earth and S'frome to be rest frome of muon

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Test: Classical Mechanics - 1 - Question 12

A comet in an orbit about the sun has a velocity 10km/sec at aphelion and 80km/sec at perihelion if the earth's velocity in a circular orbit is 30 km/sec and the radius of its orbit is 1.5 x 108km, the aphelion distance Ra for comet is ____ x 108km. (Nearest integer)

Detailed Solution for Test: Classical Mechanics - 1 - Question 12

Let v be velocity of the earth, R the radius of the earth

applying conservation of energy and the angular momentum of comet

Test: Classical Mechanics - 1 - Question 13

Find Lagrangian of the pendulum of mass m and length R attached to a spring, the other end of which is fixed at the bottom as shown in the figure. The length of the undeformed spring is l

Detailed Solution for Test: Classical Mechanics - 1 - Question 13

Lagrangian, L = T - V

Test: Classical Mechanics - 1 - Question 14

The kinetic energy  of a particle in terms of coordinate r and q = sin θ, where r & θ are polar coordinate is

Detailed Solution for Test: Classical Mechanics - 1 - Question 14

Kinetic energy of particle

Test: Classical Mechanics - 1 - Question 15

Consider the At wood's machine. Let x and y be the vertical position of the middle mass and right mass, respectively with upward  taken to be positive. The  conjugate momenta, Px and Py respectively,  are

Detailed Solution for Test: Classical Mechanics - 1 - Question 15

If the right two masses move up by x and y then the left mass move down by (x+y)/2
∴ Lagrangian

Test: Classical Mechanics - 1 - Question 16

If Iij is the tensor of inertia of a solid sphere, x2+y2+z2 = a2, of mass M in the first octant, then

Detailed Solution for Test: Classical Mechanics - 1 - Question 16

In first quadrant,  dm = pdx dy dz

Test: Classical Mechanics - 1 - Question 17

A train with proper length L moves with speed 5c/13 with respect to the ground. A ball is thrown from the back of the train to the front. The speed of the ball with respect to the train is c/3. As viewed by someone on the ground how much time does the ball spend in the air and how far does it travel.

Detailed Solution for Test: Classical Mechanics - 1 - Question 17

Test: Classical Mechanics - 1 - Question 18

The force of interaction between a particle of mass m1 and a second particle of mass m2 separated by a distance r is given by an attractive gravitational force and a repulsive force that is proportional to r-3, with probability constant C,

the angular frequency of small oscillation about the stable equilibrium position is

Detailed Solution for Test: Classical Mechanics - 1 - Question 18

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Test: Classical Mechanics - 1 - Question 19

A disk of mass m and radius R is attached to a spring of constant K as shown in the figure. The disk rolls and forth without slipping. The angular frequency of the motion of the disk is  The value of α is ______.

Detailed Solution for Test: Classical Mechanics - 1 - Question 19

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Test: Classical Mechanics - 1 - Question 20

The particle of mass m and angular momentum L2 = 10mV0R2 moves in a potential

The radius of the stable circular orbit is _____R.

Detailed Solution for Test: Classical Mechanics - 1 - Question 20

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