Tag: physics

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Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

The energy of electron in an excited hydrogen atom is -3.4 eV. Its angular momentum according to Bohr's theory will be:

  1. $\cfrac{h}{\pi }$

  2. $\cfrac{h}{2\pi }$

  3. $\cfrac{3h}{2\pi }$

  4. $\cfrac{2h}{\pi }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$E=\dfrac{-13.6}{n^{2}}eV$

$\dfrac{-13.6}{n^{2}}=\ 3.4 $
$\Rightarrow    n = 2$
So, its angular momentum $=\dfrac{nh}{2\pi }$ $=\dfrac{2h}{2\pi }$ $=\dfrac{h}{\pi }$

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

Under the action of a central force, there is a conservation of-

  1. Angular momentum only

  2. Mechanical energy only

  3. Angular momentum and mechanical energy

  4. Neither angular momentum nor mechanical energy
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Under the action of a central force, there is a conservation ofAngular momentum and mechanical energy.

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

Four particles of masses in the ratio 1:2:3:4 are rotating in concentric circles of radii proportional to their masses with the same angular velocity. What is the angular momentum of the system

  1. $4mw^2r$

  2. $10mw^2r$

  3. $30mw^2r$

  4. $20mw^2r$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The angular momentum of a single particle is $mw^2r$. If there are 4 particles, we can write,
$L _{tot}=mw^2r+2mw^2(2r)+3mw^2(3r)+4mw^2(4r)=30mw^2r$

The correct option is (c)

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

Two identical particles of mass m move in a circle of radius r , 180 degrees out of phase at an angular speed  $\omega$ about the z-axis in a plane parallel to but a distance h above the x-y plane (Figure 19.14). Find the magnitude and the direction of the angular momentum L relative to the origin.

  1. $2mr^2w$

  2. $mr^2w$

  3. zero

  4. $mr^2w/2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For two particles at distance r from the z-axis, 180 degrees apart, the angular momentum about the origin (z-axis) is L = 2 * mvr = 2 * mr(rw) = 2mr^2w.

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

Two identical particles of mass m are separated by a distance of 1 metre each and are rotating with a constant speed of 5 m/s . What will be their angular momentum about an axis distant 0.8 m from the first particle on the line joining them

  1. 5m

  2. 3m

  3. 2m

  4. m
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

A particle is in uniform circular motion in a   horizontal plane. Its angular momentum is constant when the origin is taken at

  1. centre of the circle

  2. any point on the circumference of the circle.

  3. any point inside the circle.

  4. any point outside the circle.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For uniform circular motion, the angular momentum L = r x p is constant only when the origin is at the center of the circle, as r and p are perpendicular and their magnitudes are constant.

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

A particle starts from the point 0.8 m and moves with a uniform velocity of 3 m/s. what is the angular momentum of the particle after 5 seconds about origin.mass of the particle is 1  kg.

  1. $12kgm^2$/s

  2. $24 kgm^2/s$

  3. $32 kgm^2/s$

  4. $44 kgm^2/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The correct option is B

Given,

$mass=1kg$

$t=5s$

$velocity=3m/s$

The angular momentum of the particle about a fixed position is given by:

$L = r \times mV$

So it is the product of momentum of a particle and its perpendicular distance from the fixed position.


Here particle is moving along the x-direction



So its momentum is along the x-direction

$P = mv = 1\times3 = 3 kgm/s$

Now, the perpendicular distance from origin to the momentum of particle is:

$r = 8 m$

Now, angular momentum is


$L = 8\times3 = 24 kg m^2/s$

So angular momentum is $ 24 kg m^2/s$
Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t)=2t^{3}-6t^{2}$. The torque on the wheel becomes zero at :

  1. $t=1s$

  2. $t=0.5\ s$

  3. $t=0.25\ s$

  4. $t=2s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given, $\theta (t)=2t^3-6t^2$

We, know $T=\propto \dfrac{Id^2 \theta}{dt^2}=I\dfrac{d}{dt}(\dfrac{d \theta}{dt})=I\dfrac{d}{dt}(6t^2-12t)=I(12t-12)=0$

Then, $12t-12=0\Rightarrow t=1s$

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

Let $A$ be the area swept by the line joining the earth and the sun during Feb 2012. The area swept by the same line during the first week of that month is

  1. $\dfrac{A}{4}$

  2. $\dfrac{7A}{29}$

  3. $A$

  4. $\dfrac{7A}{30}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Kepler's second law states that the radius vector sweeps out equal areas in equal times. February 2012 had 29 days. The area swept in 7 days is 7/29 of the total area.

Multiple choice physics rotational motion of a rigid body and moment of inertia angular momentum (l) and conservation of angular momentum angular momentum in case of rotation about a fixed axis law of conservation of angular momentum

(i) Linear momentum is proportional to $1/n$
(ii) Radius is proportional to $n$
(iii) Kinetic energy is proportional to $1/n^{2}$
(iv) Angular momentum is proportional to $n$
Choose the correct option from the codes given below. 

  1. $(i),(iii),(iv)$ are correct

  2. $(i)$ is correct

  3. $(i),(ii)$ are correct

  4. $(iii)$ is correct
Reveal answer Fill a bubble to check yourself
C Correct answer