Tag: physics

Quizzes (598) Questions (13441)

Questions Related to physics

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 position of a particle is given by $\overrightarrow { r } =(\hat{i} +2\hat{j} -\hat{k})$ and momentum $\overrightarrow { P } =(3\hat{i} +4\hat{j} -2\hat{k})$. The angular momentum is perpendicular to

  1. X-axis

  2. Y-axis

  3. Z-axis

  4. Line at equal angles to all the three axes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,

$\vec r=\hat i+2\hat j-\hat k$
$\vec P=3\hat i+4\hat j-2\hat k$
Angular momentum, $\vec L=\vec r \times \vec P$
$\vec L=(\hat i+2\hat j-\hat k)\times (3\hat i+4\hat j-2\hat k)$
$\vec L=0\hat i-\hat j-2\hat k$
Hence, The angular momentum is perpendicular to the X-axis.
The correct option is A.

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 of mass $1\ kg$ is projected at an angle $ \theta $ with horizontal. Its co-ordinates at any instant are $(5m,5m)$ and itis having velocity components along $X- $axis and $Y-$axis as $8\ m/s$ and $4\ m/s$ respectively. Its angular momentum about the origin is 

  1. $- 20\ N-m$ $ \hat{k} $

  2. $+ 20\ N-m$ $ \hat{k} $

  3. $- 60\ N-m$ $ \hat{k} $

  4. $+ 60\ N-m$ $ \hat{k} $
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 of mass m = 5 units is moving with a uniform speed v = $3\sqrt2$ units in the XY - plane along the line y = x + 4.The magnitude of the angular momentum about origin is  

  1. zero

  2. 60 unit

  3. 7.5 unit

  4. $40\sqrt2$ unit
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

L = m * v * d, where d is the perpendicular distance from the origin to the line y = x + 4 (or x - y + 4 = 0). d = |0 - 0 + 4| / sqrt(1^2 + (-1)^2) = 4 / sqrt(2) = 2 * sqrt(2). L = 5 * (3 * sqrt(2)) * (2 * sqrt(2)) = 5 * 3 * 2 * 2 = 60.

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 angular momentum of an electron in a hydrogen atom is proprotional to ( where r is redius of orbit) 

  1. $\frac{1}{\sqrt{r}}$

  2. $\frac{1}{r}$

  3. $r^{1/2}$

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

Radius of the nth orbit rn ∝ n2/Z      ⇒    n ∝ (r n)½

Angular momentum Ln = nh/(2π) ∝ (r n)½

$=r^{1/2}$

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

If a particle of mass m is moving with constant velocity V parallel to X-axis along $y=axis$. The angular momentum with respect to origin at any time 't' is

  1. $mV\hat{J}$

  2. $-mVa\hat{K}$

  3. $mV\hat{K}$

  4. $mVa\hat{J}$
Reveal answer Fill a bubble to check yourself
A 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

The rotational kinetic energy of a hollow spherical shell 2.5 J. If its frequency of rotation is made 10 times, then new kinetic energy will be -

  1. $0.25 J$

  2. $2.5\times { 10 }^{ 2 }J$

  3. $2500 J$

  4. $2.5 J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The rotational kinetic energy is given by
$K=\dfrac{1}{2}mr^2\omega ^2=2.5 J$. . . . .(1)
If frequency of rotation made 10 times , then the new rotational kinetic energy is
$K'=\dfrac{1}{2}mr^2 \times 10^2\omega ^2$
$K'=100K$ 
$K'=2.5\times 10^2J$
The correct option is B.
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 angular momentum of an electron revolving in a circular orbit is J, What is its magnetic moment? 

  1. $\frac{mJ}{2e}$

  2. $\frac{eJ}{2m}$

  3. $\frac{2m}{eJ}$

  4. $\frac{emJ}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to Bohr modal of hydrogen like atoms, negatively charged electrons revolves around the positively charged nucleus. This uniform circular motion of electrons is equivalent to a current loop which possesses a magnetic dipole moment =IA

I:- current in the loop

A:-area

Consider an electron revolving anticlockwise around a nucleus in an orbit of radius r with speed v and time period T.

Equivalent current,

I= charge/time

=e/t = e/2πr/v

=ev/2πr

Area of current loop ,A=πr2

So , orbital magnetic moment of electron is=IA

=(ev/2πr). πr2

=evr/2

As J is angular momentum. J=mvr

m- mass of electron

So orbital magnetic moment = eJ/2m

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

$E _n$ and $J _n$ denote the total energy magnitude and the  angular momentum of an electron in the nth allowed orbit of the Both atom .Then:

  1. $E _n \pi J _n$

  2. $E _n \pi \frac {1} {J}$

  3. $E _n \pi { J } _{ n }^{ 2 }$

  4. $E _n \pi \frac {1} {J^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the Bohr model, E is proportional to 1/n^2 and J (angular momentum) is proportional to n. Therefore, E is proportional to 1/J^2.

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 wooden block of mass $2\ m$ is hung with the help of a light string of length $l$ in the vertical plane.
A bullet of mass $\dfrac{m}{4}$ moving horizontally with velocity $v _{0}\left(v _{0}=\sqrt{5gl}\right)$ penetrates the block and comes out with velocity $\dfrac{v _{0}}{2}$. The maximum height reached by the block is (Assume string remains vertical till bulled passes through the block)

  1. $\dfrac{{v} _{0}^{2}}{256\ g}$

  2. $\dfrac{{v} _{0}^{2}}{128\ g}$

  3. $\dfrac{{v} _{0}^{2}}{512\ g}$

  4. $\dfrac{{v} _{0}^{2}}{32\ g}$
Reveal answer Fill a bubble to check yourself
B Correct answer