Tag: physics

Questions Related to physics

A stone tied to one end of the string is revolved round a rod in such a way that the string winds over the rod and get shortened. In this process which of the following quantities remain 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. Moment of inertia

  2. Momentum

  3. Angular momentum

  4. Kinetic energy

Show answer
Correct Option: C
Explanation:

As the distance between the stone and the rotational axis is changing the moment of inertia thus changes. Momentum keeps on changing around the circular path. As the moment of inertia  changes we see that the kinetic energy changes too. The angular momentum is the only conserved quantity since there is no external torque acting on the stone.

A swimmer while jumping into water from a height easily forms a loop in air, if

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. He pulls his arms and leg in

  2. He spreads legs and his arms

  3. He keeps himself straight

  4. His body is so formed

Show answer
Correct Option: A
Explanation:

by pulling his arms and legs in he decreases his moment of inertia, thereby increasing his angular velocity using the principle of conservation of angular momentum.

If no external force acts on a system

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. Velocity of centre of mass remains constant

  2. Total kinetic energy of the system remains constant

  3. Angular momentum of system may change

  4. Total mechanical energy of the system remains constant

Show answer
Correct Option: A
Explanation:

No force means no acceleration implying constant velocity. Also as velocity is constant kinetic energy remains constant. The angular momentum may change due to the change in moment of inertia. Also the total mechanical energy may change due the change in potential energy.

Two loops P and Q are made from a uniform wire. The radii of P and Q are $r _1$ and $r _2$ respectively, and their moments of inertia about their own axises are $I _1$ and $I _2$ respectively. If $I _2 = 4I _1$, the $r _1/r _2$ equals:

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. $4^{2/3}$

  2. $4^{1/3}$

  3. $4^{7/3}$

  4. $4^{-1/3}$

Show answer
Correct Option: C

A particle moves on a circular path with decreasing speed. Choose the correct statement.

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. Angular momentum remains constant.

  2. Acceleration $\vec{a}$ is towards the centre.

  3. Particle moves in a spiral path with decreasing radius.

  4. The direction of angular momentum remains constant.

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Correct Option: C

A particle of mass 2 kg located at the position $ \left( \hat { i } +\hat { j }  \right) m $ has a velocity $ 2\left( \hat { i } -\hat { j } +\hat{ k } \right) ms^{-1} $ . Its angular momentum along z-axis in $ kgm^2 s^{-1}  $ 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. $-8$

  2. $+8$

  3. $-4$

  4. zero

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Correct Option: A

Angular momentum of a system a particles changes, when

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. Force acts on a body

  2. Torque acts on a body

  3. Direction of velocity changes

  4. None of these

Show answer
Correct Option: B
Explanation:

If we apply a torque on a body, then angular momentum of the body changes according to the relation
$\bar{\tau} = \displaystyle\frac{d\bar{L}}{dt} \Rightarrow if \space \bar{\tau} = 0$ then, $\overrightarrow{L} = constant$

A gymnast takes turns with her arms & legs stretched. When she pulls her arms & legs in

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 decreases

  2. The moment of inertia decreases

  3. The angular velocity stays constant

  4. The angular momentum increases

Show answer
Correct Option: B
Explanation:

Since no external torque act on gymnast, so angular momentum $(L =

I\omega)$ is conserved. After pulling her arms & legs, the angular velocity increases but moment of inertia of gymnast, decreases in, such a way that angular momentum remains constant.

If a running boy jumps on a rotating table, which of the following is conserved?

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. Linear momentum

  2. K.E

  3. Angular momentum

  4. None of these

Show answer
Correct Option: C
Explanation:

The boy does not exert a torque to rotating table by jumping, so angular momentum is conserved i.e., 
$\displaystyle\frac{d\bar{L}}{dt} = 0 \Rightarrow \bar{L} = constant$

In which of the following case(s), the angular momentum is conserved ?

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 planet Neptune moves in elliptical orbit around the sun with sun at one focus

  2. A solid sphere rolling on an inclined plane

  3. An electron revolving around the nucleus in an elliptical orbit

  4. An $\alpha $ particle approaching a heavy nucleus from sufficient distance.

Show answer
Correct Option: A,C,D
Explanation:

Angular momentum is conserved if net external torque is zero
(A) torque about sun is zero , $\because$ line of focus passer though it and no external force is present.
(B) Torque of friction is present 
(C) Force on the electron is internal , $\therefore$ torque is zero 
(D) No external force is present which may produce changes in angular momentum.