Angular Acceleration

Q. A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A$. The rod is released from rest in horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{m{l}^2}{3}$. The initial angular acceleration of the rod will be

1. $\frac{2g}{3l}$
2. $\frac{mgl}{2}$
3. $\frac{3gl}{2}$
4. $\frac{3g}{2l}$

Q.

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope?

Q. In the arrangement shown in the figure a block of mass $m=2kg$ lies on a wedge of mass $M=8kg$. The initial acceleration of the wedge (if the surfaces are smooth) given by $\frac{3\sqrt{3}g}{x}m{s}^{-2}$, then $x$ is.

Q. A wheel is rolling on a horizontal plane. At a certain instant, it has a velocity ${}^{\prime }{v}^{\prime }$ and acceleration ${}^{\prime }{a}^{\prime }$ of CM as shown in figure. Acceleration of

1. $A$ is vertically upwards
2. $B$ may be vertically downwards
3. $C$ cannot be horizontal
4. some points on the rim may be horizontal leftwards

Q. In figure (i), half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at $O$ and a force $F$ is applied at the end of steel part. In figure (ii), the steel part is pivoted at $O$ and the same force is applied at the wooden end.

1. More angular acceleration will be produced in (i)
2. More angular acceleration will be produced in (ii)
3. Same angular acceleration will be produced in both the conditions
4. Information is incomplete

Q. Assertion :An electric lamp is connected in series with a long solenoid of copper with air core and then connected to an ac source. If an iron rod is inserted in the solenoid, the lamp will become dim. Reason: If an iron rod is inserted in the solenoid, the inductance of the solenoid increases.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first 2 sec, it rotates through an angle ${\theta }_1$. In the next 2 sec, it rotates through an additional angle ${\theta }_2$ . The ratio of angles is

1. 1
2. 2
3. 3
4. 5

Q. If vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are respectively equal to $3\hat{i}-4\hat{j}+5\hat{k}$ and $2\hat{i}+3\hat{j}-4\hat{k}$, find the unit vector parallel to $\overrightarrow{A}+\overrightarrow{B}$

1. $5\hat{i}-\hat{j}+\hat{k}$
2. $\frac{5\hat{i}-\hat{j}+\hat{k}}{3\sqrt{3}}$
3. $5\hat{i}+\hat{j}-\hat{k}$
4. $\frac{5\hat{i}+\hat{j}-\hat{k}}{3\sqrt{3}}$

Q. A small block is connected to a massless rod placed on a fulcrum, which in turn is attached to a spring of force constant $k$ as shown in the figure. The block is displaced down slightly, and left free. Find time period of small oscillations.

1. $2\pi \left(\frac{b}{a}\right)\sqrt{\frac{m}{k}}$
2. $2\pi \left(\frac{a}{b}\right)\sqrt{\frac{m}{k}}$
3. $2\pi \left(\frac{b}{a}\right)\sqrt{\frac{k}{m}}$
4. $2\pi \left(\frac{a}{b}\right)\sqrt{\frac{k}{m}}$

Q. A wheel is making rotations about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rot/s in 4 seconds. It's angular acceleration is

1. $50\frac{rot}{s^2}$
2. $25\frac{rot}{s^2}$
3. $40\frac{rot}{s^2}$
4. $500\pi \frac{radians}{s^2}$

Q. Tangential acceleration is

1. a measure of how quickly the tangential velocity changes
2. a measure of how quickly the acceleration of the particle undergoing circular motion changes
3. a measure of how quickly the normal velocity changes in a circular motion
4. a measure of how quickly the angle between the path of the particle and the centripetal force changes

Q. A rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha -\beta t$, at time $t$ where $\alpha ,\beta$ are constants. The angle through which it rotates before it stops:

Q. A beaker of liquid accelerates from rest, on a horizontal surface, with acceleration $a$ to the right.
Which edge of the water surface is higher?

Q. A solid cylinder of mass $2$ Kg and radius $0.2$ m is rotating about its own axis without friction with angular velocity $3$ rad/s. A particle of mass $0.5$ Kg and moving with a velocity of $5$m/s strikes the cylinder and sticks to it as shown in. The velocity of the system after the particle sticks it will be

1. $5.3$ radians/sec
2. $0.3$ radians/sec
3. $8.3$ Radians/sec
4. $10.3$ radians/sec

Q. A body is projected from the ground for horizontal range $100m$. At the highest point of its path it breaks apart into two identical part $P$ and $Q$. If $P$ comes to rest, than the horizontal distance of the landing point of part $Q$, from the point of projection is:

1. $200m$
2. $250m$
3. $150m$
4. $50m$

Q. At low speed, a fan blade is turning at 80 rad/s clockwise. The fan is turned up a notch to rotate at 125 rad/s clockwise. If the time to change speeds is 0.5 s, find the angular acceleration of the fan blades

Q. The diameter of a flywheel is $1.2m$ and it makes 900 revolutions per minute. Calculate the acceleration at a point on its rim.

1. $540{\pi }^{2}m/s^2$
2. $324m/s^2$
3. $360{\pi }^{2}m/s^2$
4. $540m/s^2$

Q. A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta }_1$ in first one second and through an additional angle ${\theta }_2$ in the next one second. The ratio ${\theta }_2/{\theta }_1$ is:

1. $4$
2. $2$
3. $1$
4. $3$

Q. Two identical particles of mass $m$ carry charge $Q$ each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed $v$. The closest distance of approach will be

1. $\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{mv}$
2. $\frac{1}{4\pi {\epsilon }_0}\frac{{4Q}^2}{mv}$
3. $\frac{1}{4\pi {\epsilon }_0}\frac{{4Q}^2}{m{v}^2}$
4. $\frac{1}{4\pi {\epsilon }_0}\frac{{2Q}^2}{m{v}^2}$

Q. In the figure, s sphere of radius $2m$ rolls on a plank. The accelerations of the sphere and the plank are indicated. The value of $\alpha$ is

1. $2rad/s^2$
2. $4rad/s^2$
3. $3rad/s^2$
4. $1rad/s^2$

Q. The rms value of current $I_{rms}$ is
(where, $I_0$ is the value of peak current)

1. $\frac{I_0}{2\pi }$
2. $\frac{I_0}{\sqrt{2}}$
3. $\frac{2I_0}{\pi }$
4. $\sqrt{2}{I}_0$

Q. A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A$. The rod is released from rest in horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{m{l}^2}{3}$. The initial angular acceleration of the rod will be

1. $\frac{2g}{3l}$
2. $\frac{mgl}{2}$
3. $\frac{3gl}{2}$
4. $\frac{3g}{2l}$

Q. A fan is rotating with angular velocity 100 rev s${}^{-1}$. Then it is switched off. It takes $5$ min to stop.
a. Find the total number of revolution made before the fan stops. (assume uniform angular retardation)
b. Find the value of angular retardation.
c. Find the average angular velocity during this interval.

1. a. $\theta =15000rev.$
   b. $\alpha =\frac{1}{3}rev{s}^{-2}$
   c. $50rev{s}^{-1}$
2. a. $\theta =16000rev.$
   b. $\alpha =\frac{1}{3}rev{s}^{-2}$
   c. $50rev{s}^{-1}$
3. a. $\theta =15000rev.$
   b. $\alpha =\frac{1}{2}rev{s}^{-2}$
   c. $50rev{s}^{-1}$
4. a. $\theta =15200rev.$
   b. $\alpha =\frac{1}{3}rev{s}^{-2}$
   c. $50rev{s}^{-1}$

Q. A particle is tied to one end of string and is whirled in a circle. If the string breaks, the particle files off tangentially. Why?

Q. Two springs with negligible masses and force constant of $K_1=200N{m}^{-1}$ and $K_2=160N{m}^{-1}$ are attached to the block of mass $m=10kg$ as shown in the figure.Initially the block is at rest , at the equilibrium position in which both springs are neither stretched nor compressed.At time $t=0,$ a sharp impulse of $50Ns$ is given to the block with a hammer

1. Period of oscillations for the mass m is $\frac{\pi }{6}s$
2. Maximum velocity of the mass $m$ during its oscillation is $10m{s}^{-1}$
3. Data are insufficient to determine maximum velocity
4. Amplitude of oscillation is $0.83m$

Q. A body executes SHM under the influence to one force and has time period ${}^{\prime }{T}_1^{\prime }$ seconds and the same body executes SHM with period ${}^{\prime }{T}_2^{\prime }$ seconds when under the influence of another force. When both forces act simultaneously and in the same direction then the time period of the same body is?

1. $(T_1+T_2)\sec$
2. $\sqrt{T_1^2+T_2^2}\sec$
3. $\sqrt{\frac{T_1+T_2}{T_1{T}_2}}\sec$
4. $\sqrt{\frac{T_1^2{T}_2^2}{(T_1^2+T_2^2)}}\sec$

Q. Assertion :Magnetic field due to current carrying solenoid is independent of its length and cross-sectional area. Reason: The magnetic field inside the solenoid is uniform.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. If $I,a$ and $t$ are the moment of inertia, angular acceleration and torque respectively of a body rotating about any axis with angular velocity $\omega$, then

1. $t=Ia$
   
2. $t=I\omega$
   
3. $I=t\omega$
   
4. $a=I\omega$
   

Q. If most of the population on earth is migrated to poles of earth then the time duration of a day :

1. Remains same
2. Decreases
3. Increases
4. First increases then decreases

Q. A rod of length is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod is $a$ and $b$ respectively. The angular acceleration of rod at this instant will be:

1. $\frac{a+b}{l}$
2. $\frac{\sqrt{|a^2-b^2|}}{l}$
3. $\frac{\sqrt{a^2+b^2}}{l}$
4. $Noneofthese$