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Title & Summary Author Updated

### Execl Sheet of Listing of students

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

### Course Feedback Form

Feedback for cyber shiksha  java course.

Aashutosh 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 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 anarrow?
kapoor 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 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 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 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 20/10/19

### MidSemester Examination

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

### Weekly Quiz and Exam Papers

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