Physics (Mechanics & Mechanics of Solid)

The moment of inertia of an arbitrarily shaped rigid body is a

The curl of a gradient is

In a lightly damped oscillator the frequency

As opposed to a standing bicycle a moving bicycle does not fall easily because

The Foucault pendulum undergoes precession because of

Which of the following is NOT Kepler's law

Which of the following is not true for conservative force

The Newton's law gives the relationship between force, mass and

Velocity or energy resonance in the forced oscillator take place when

Where $ \omega $ is frequency of force, $ \omega_0 $ is natural frequency of the oscillator and $ 2b = \frac{B}{m} $ is damping coefficient

A spinning top is an example of

State the definition of scalar and vector quantities. Explain how they transform under rotation.

Under an anti-clockwise rotation by an angle $ \theta $ of a 2d Cartesian coordinate system find out the transformation rules for the components of an arbitrary vector $ \vec{A} $. Show that the scalar product $ \vec{A} \cdot \vec{B} $ is invariant under rotation of the coordinate system.

Define inertial and non-inertial frames. Explain the meaning of fictitious force

Derive an expression for acceleration in a rotating frame and obtain the centripetal and Coriolis terms in the acceleration. Explain briefly how the Coriolis forces are useful in explaining the weather system

Show that the conservative force acting on a particle is always perpendicular to the equipotential surface.

Prove that the work done by a force which is the gradient of a potential ($ \vec{F} = -\nabla U $) is path independent.

The potential function is given as $ U = -2x - z^2 $. Find the work done by the resulting force in moving a particle from the origin to a point (2,2,2) along a straight line.

Explain overdamped, underdamped and critically damped harmonic motion.

Write an equation for a forced harmonic oscillator and obtain the conditions of resonance.

Derive the moment of inertia tensor of a rigid body and explain the concept of principal axes.

A uniform solid disc of mass $ M $ and radius $ R $ having moment of inertia $ MR^2/2 $ about an axis passing through its centre has initial uniform angular velocity. A constant friction force of magnitude $ f $ is then applied on the rim in tangential direction so that the disc finally comes to a stop in time $ T $. Find the magnitude of the friction force.

Derive the conditions for elliptic, hyperbolic and parabolic orbits in central force motion.

Show that the total angular momentum of a solid body can be written as the sum of the angular momentum of the centre of mass and the angular momentum about the centre of mass

Derive Euler's equations for the rotational motion of a rigid body and explain its importance.

Prove that the angular momentum is conserved in a central force motion and that the orbit of the particle is always planar.

The moment of inertia of an arbitrarily shaped rigid body is a

The curl of a gradient is

In a lightly damped oscillator the frequency

As opposed to a standing bicycle a moving bicycle does not fall easily because

The Foucault pendulum undergoes precession because of

Which of the following is NOT Kepler's law

Which of the following is not true for conservative force

The Newton's law gives the relationship between force, mass and

Velocity or energy resonance in the forced oscillator take place when

Where $ \omega $ is frequency of force, $ \omega_0 $ is natural frequency of the oscillator and $ 2b = \frac{B}{m} $ is damping coefficient

A spinning top is an example of

State the definition of scalar and vector quantities. Explain how they transform under rotation.

Under an anti-clockwise rotation by an angle $ \theta $ of a 2d Cartesian coordinate system find out the transformation rules for the components of an arbitrary vector $ \vec{A} $. Show that the scalar product $ \vec{A} \cdot \vec{B} $ is invariant under rotation of the coordinate system.

Define inertial and non-inertial frames. Explain the meaning of fictitious force

Derive an expression for acceleration in a rotating frame and obtain the centripetal and Coriolis terms in the acceleration. Explain briefly how the Coriolis forces are useful in explaining the weather system

Show that the conservative force acting on a particle is always perpendicular to the equipotential surface.

Prove that the work done by a force which is the gradient of a potential ($ \vec{F} = -\nabla U $) is path independent.

The potential function is given as $ U = -2x - z^2 $. Find the work done by the resulting force in moving a particle from the origin to a point (2,2,2) along a straight line.

Explain overdamped, underdamped and critically damped harmonic motion.

Write an equation for a forced harmonic oscillator and obtain the conditions of resonance.

Derive the moment of inertia tensor of a rigid body and explain the concept of principal axes.

A uniform solid disc of mass $ M $ and radius $ R $ having moment of inertia $ MR^2/2 $ about an axis passing through its centre has initial uniform angular velocity. A constant friction force of magnitude $ f $ is then applied on the rim in tangential direction so that the disc finally comes to a stop in time $ T $. Find the magnitude of the friction force.

Derive the conditions for elliptic, hyperbolic and parabolic orbits in central force motion.

Show that the total angular momentum of a solid body can be written as the sum of the angular momentum of the centre of mass and the angular momentum about the centre of mass

Derive Euler's equations for the rotational motion of a rigid body and explain its importance.

Prove that the angular momentum is conserved in a central force motion and that the orbit of the particle is always planar.