Classical Mechanics (GATE Physics): Questions 8 - 11 of 38

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Question number: 8

» Classical Mechanics » Kepler Problem and Planetary Motion

Appeared in Year: 2014

MCQ▾

Question

A planet of mass m moves in a circular orbit of radius r0 in the gravitational potential (r)=kr , where k is a positive constant. The orbital angular momentum of the planet is –

Choices

Choice (4) Response
a.

r0km

b.

2r0km

c.

r0km

d.

2r0km

Question number: 9

» Classical Mechanics » Mechanics of System of Particles

Appeared in Year: 2015

Short Answer Question▾

Write in Short

A particle of mass 0.01kg falls freely in the earth’s gravitational field with an initial

velocity v(0)=gravitationalfieldwithaninitialvelocity10ms . If air exerts a friction force of form, f=kv , then for k=0.05Nsm , the velocity (inms) at time t=0.2s is ________ (up to two decimal places). (Use g=10ms2 and e=2.72 )

Question number: 10

» Classical Mechanics » Small Oscillations and Normal Modes

Appeared in Year: 2016

Short Answer Question▾

Write in Short

Two blocks are connected by a spring of spring constant k . One block has mass m and the other block has mass 2m . If the ratio km=4s2 , the angular frequency of vibration ω of the two block spring system in s1 is _ . (Give your answer up to two decimal places)

Question number: 11

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

Appeared in Year: 2015

MCQ▾

Question

The Lagrangian for a particle of mass m at a position r moving with a velocity v is given by L=m2v2+CrvV(r) , where V(r) is a potential and C is a constant. If pc is the canonical momentum, then its Hamiltonian is given by,

Choices

Choice (4) Response
a.

12m(pcCr)2+V(r)

b.

pc22m+V(r)

c.

12mpc2+C2r2+V(r)

d.

12m(pc+Cr)2+V(r)

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