Angular momentum and its conservation — practice questions

Question 1 · difficulty L2 · understanding

When the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ changes sign as $-\vec{r}$, which one of the following vector will not flip under sign change?

• A. Velocity
• B. Linear momentum
• C. Acceleration
• D. Angular momentum

Question 2 · difficulty L2 · understanding

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector as $\vec{r}=a(\hat{i} \cos \omega t+\hat{j} \sin \omega t)$. The direction of force is

• A. Opposite to the direction of $\vec{L}$
• B. Opposite to the direction of $\vec{L} \times \vec{P}$
• C. Opposite to the direction of $\vec{r}$
• D. Opposite to the direction of $\vec{P}$

Question 3 · difficulty L2 · understanding

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R : Fan continues to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below.

• A. A is not correct but R is correct
• B. A is correct but R is not correct
• C. Both A and R are correct and R is the correct explanation of A
• D. Both A and R are correct but R is NOT the correct explanation of A

Question 4 · difficulty L2 · understanding

Angular momentum of a single particle moving with constant speed along circular path :

• A. changes in magnitude but remains same in the direction
• B. remains same in magnitude and direction
• C. remains same in magnitude but changes in the direction
• D. is zero

Question 5 · difficulty L2 · understanding

A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $$\omega$$. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :

• A. $$\omega {M \over {M + m}}$$
• B. $$\omega {{M + 2m} \over M}$$
• C. $$\omega {M \over {M + 2m}}$$
• D. $$\omega {{M - 2m} \over {M + 2m}}$$

Question 6 · difficulty L2 · understanding

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

• A. Linear momentum of the system does not change in time.
• B. Kinetic energy of the system does not change in time.
• C. Angular momentum of the system does not change in time.
• D. Potential energy of the system does not change in time.

Question 7 · difficulty L3 · understanding

A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $\left(\omega_1\right)$ about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $\mathrm{R} / 2$ is $x \omega_1$. The value of $x$ is _________.

Question 8 · difficulty L3 · understanding

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and length $30 \mathrm{~cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2 \mathrm{~Ns}$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi}{x} \mathrm{~s}$, where $x=$ _______ .

Question 9 · difficulty L3 · understanding

A body of mass '$$m$$' is projected with a speed '$$u$$' making an angle of $$45^{\circ}$$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $$\frac{\sqrt{2} m u^3}{X g}$$. The value of '$$X$$' is _________.

Question 10 · difficulty L3 · understanding

Two discs of moment of inertia $$I_1=4 \mathrm{~kg} \mathrm{~m}^2$$ and $$I_2=2 \mathrm{~kg} \mathrm{~m}^2$$, about their central axes & normal to their planes, rotating with angular speeds $$10 \mathrm{~rad} / \mathrm{s}$$ & $$4 \mathrm{~rad} / \mathrm{s}$$ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is _________ J.