Tag: physics

Questions Related to physics

Choose the INCORRECT statements

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

  1. If Linear momentum of system is conserved then angular momentum of system must be also conserved.

  2. If angular momentum is conserved then angular velocity must be also conserved about the same axis.

  3. If not torque about any axis is zero then force must also be zero.

  4. If a rigid body is in translational equilibrium then its linear velocity is constant but angular velocity may be varying

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Correct Option: D

A satellite with a mass of $M$ moves in a circular orbit of radius $R$ at a constant speed of $v$. Which of the following must be true?
(I) The net force on the satellite is equal to MR and is directed toward the centre of the orbit,
(II) The net work done on the satellite by gravity in one revolution is zero.
(III) The angular momentum of the satellite is constant.

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

  1. I only

  2. III only

  3. I and II only

  4. II and III only

  5. I, II and III

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Correct Option: C

A circular ring of mass $1$ Kg and radius $0.2$ m executes $10$ revolutions per sec. Its angular momentum would be -$( kg-m^2/sec)$

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

  1. $0.025$

  2. $0.25$

  3. $2.5$

  4. $25$

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Correct Option: B

The total angular momentum of a body is equal to the angular momentum  of its center of mass if the body has:

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

  1. only rotational motion

  2. only translational motion

  3. both rotational and translational motion

  4. no motion at all

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Correct Option: C

 Two bodies of different masses have same K.E. The one having more momentum is

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

  1. Heavier body

  2. lighter body

  3. both none

  4. both

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Correct Option: B
Explanation:

$K.E.$ for a given momentum is inversely proportional to the mass$.$

So$,$ the lighter mass has greater kinetic energy$.$ For two bodies having same kinetic energy$,$ the heavier one has greater momentum$.$
Hence,
option $(B)$ is correct answer.  

A force $\vec F = \alpha \hat i + 3\hat j + 6\hat k$ is acting at a point $\vec r = 2\hat i - 6\hat j - 12\hat k$. The value of $\alpha$ for which angular momentum about the origin is conserved is:-

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

  1. $1$

  2. $-1$

  3. $2$

  4. zero

Show answer
Correct Option: B
Explanation:

Given,
$\vec r=2\hat i-6\hat j-12\hat k$
$\vec F=\alpha\hat i +3\hat j+6\hat k$
For the conservation of angular momentum about origin, the torgue acting on the particle will be zero.
$\tau=\vec r\times \vec F$
$\vec r\times \vec F=0$
$(\alpha \hat i+3\hat j+6\hat k)\times (2\hat i-6\hat j-12\hat k)=0\hat i+0\hat j+0\hat k$
$\hat i(-36+36)-\hat j (12+12\alpha)+\hat k(6+6\hat k)=0\hat i+0\hat j+\hat k$
By equating it's coefficient, we get
$12+12\alpha =0$,   $6+6\alpha =0$
$12=-12\alpha$
$\alpha =-1$
The correct option is B.

A unit mass at position vector $\vec { r } = ( 3 \hat { i } + 4 \hat { j } )$ is moving with a velocity $\vec { v } = ( 5 \hat { i } - 6 \hat { j } )$ What is the angular momentum of the body about the origin

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

  1. 2 units along $z$ -axis

  2. 38 units along $x$ -axis

  3. 38 units along $y$ -axis

  4. 38 units along $Z$ -axis

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Correct Option: C

A man standing on a platform holds weights in his outstretched arms. The system rotates freely about a central vertical axis. If he now draws the weights inwards close to his body, 

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

  1. the angular velocity of the system will increase.

  2. the angular momentum of the system will decrease.

  3. the kinetic energy of the system will increase.

  4. he will have to expend some energy to draw the weights in.

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Correct Option: A,C,D
Explanation:

When the person contracts his hands he is decreasing his moment of inertia thereby increasing his angular velocity using the principle of conservation of angular momentum $I _1\omega _1=I _2\omega _2$
As the angular velocity increases, its kinetic energy also increases. Also energy would be required to draw the weights inwards from its position.

A particle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kinetic energy halved, the angular momentum becomes:

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

  1. $2L$

  2. $4L$

  3. $ \mathrm{L} / 2 $

  4. $ \mathrm{L} / 4 $

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Correct Option: C

What is the magnitude of vertical force required to produced a moment of 20 Nm at point A (1 m, 1 m) if the force is acting at point B (2m,2m)

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

  1. 40 N

  2. 30 N

  3. 20 N

  4. 10 N

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Correct Option: C