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Execl Sheet of Listing of students

Summary (or abstract) not available for this node.
kapoor kapoor's picture 20/10/19

Problem/CM-02033

A bead of mass \(m\) slides on a frictionless wire under the influence of gravity and the shape of wire is parabolic with axis begin along the vertical upwards. The wire rotates about the its axis, (\(z\)- axis), with constant angular velocity \(\omega\). Take \(z^2=  a\rho\) as equation of the parabola.

  1. Set up Lagrangian and obtain equations of motion.
  2. Obtain the Hamiltonian. Is theHamiltonian equal to energy? Is the Hamiltonian or energy or both areconstants of motion?

 

Panat

kapoor kapoor's picture 20/10/19

Problem/ME-08005

A cart carries an air ballon suspended from ceiling and a He filled balloon tied to the floor. The figure shows the situation when the cart is moving with uniform velocity. How will the two ballons appear when the cart has an non zero acceleration in the forward direction indicated in the figure by an
arrow?
 
kapoor kapoor's picture 20/10/19

Problem/ME-12008

Consider a particle of mass \(\mu\) moving in a potential \[ V(r) = \frac{1}{2}\mu\omega^2 r^2 +\frac{\lambda^2}{2\mu r^2}. \] 

  1. Find condition on energy \(E\) and angular momentum \(L\) for circular orbits to exist.
  2. Does there exist a circular orbit for \(L=0\)?
  3. Assume orbital angular momentum \(L=0\), energy \(E= \frac{25}{2}\mu\omega^2a^2\), \(\lambda=12\mu\omega^2\) Use initial conditions \[ r(t)\big|_{t=0} = 4a;\quad \dot{r}(t)\big|_{t=0} = 0 \text{ and } \dot{\theta(t)}\big|_{t=0}=0 \] solve the equations of motion and obtain \(r\), \(\theta\) as function of time. Describe the motion that takes place under conditions specified here.
kapoor kapoor's picture 20/10/19

Problem/ME-14005

Find the moment of inertia tensor of a uniform rectangular plate w.r.t. the centre \(O\) of the plate relative to the axes \(K\) shown in figure. Use parallel axes theorem to find moment of inertia tensor relative to a set of axes \(K_2\) with origin taken as the corner \(E\). The \(Z\)- axis for both systems is perpendicular to the plate and out of the plane of paper. 
kapoor kapoor's picture 20/10/19

Problem/ME-08011

Find rotation matrix for a rotation by an angle \(\alpha\) about the axis \(1,2,1\) where \(\cos\alpha=\frac{3}{5}, \sin\alpha =\frac{4}{5}\).

kapoor kapoor's picture 20/10/19

Problem/ME-02023

Find rotation matrix for a rotation by an angle \(\alpha\) about the axis \((1,2,1)\) where \(\cos\alpha=\frac{3}{5}, \sin\alpha =\frac{4}{5}\).

kapoor kapoor's picture 20/10/19

MidSemester Examination

Summary (or abstract) not available for this node.
kapoor kapoor's picture 19/10/19

Weekly Quiz and Exam Papers

Summary (or abstract) not available for this node.
kapoor kapoor's picture 18/10/19

Problem/ME-12004

Comet Halley approaches the Sun to within 0.570 AU and its period is 75.6 years. How far from the Sun will this comet travel before it starts to return journey. Assume mass of Halley's comet is much smaller than the mass of the Sun.
[Given : 1 AU $= 1.5 \times 10^{11}$ m, $G= 6.63\times10^{-11}$ N.m\(^2\) /kg\(^2\), Mass of Sun=\( 1.99\times10^{30}\) kg ].

kapoor kapoor's picture 08/10/19

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