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Rotational Mechanics Physics - Rotational Mechanics

Rajasthan Board (RBSE) - STD 11 Science - Physics (Rajasthan - English Medium). 149 questions in this chapter.

Question types

Rotational Mechanics question types

149 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

149
Questions
6
Question groups
5
Question types
Sample Questions

Rotational Mechanics questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
A uniform rod is kept vertically on a horizontal smooth surface at a point O. If it is rotated slightly and released, it falls down on the horizontal surface. The lower end will remain:
  1. At O.
  2. At a distance less than $\frac{\text{l}}2{}$ from O.
  3. At a distance $\frac{\text{l}}2{}$ from O.
  4. At a distance larger than $\frac{\text{l}}2{}$ from O.
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Q 2M.C.Q (1 Marks)1 Mark
A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let $\overrightarrow{\text{A}}$ be a unit vector along the axis of rotation and $\overrightarrow{\text{B}}$ be the unit vector along the resultant force on a particle P of the body away from the axis. The value of $\overrightarrow{\text{A}}.\overrightarrow{\text{B}}$ is:
  1. 1
  2. -1
  3. 0
  4. None of these.
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Q 3M.C.Q (1 Marks)1 Mark
One end of a uniform rod of mass m and length (l) is clamped. The rod lies on a smooth horizontal surface and rotates on it about the clamped end at a uniform angular velocity $\omega.$ The force exerted by the clamp on the rod has a horizontal component:

  1. $\text{m}\omega^2\text{l}$

  2. $\text{Zero.}$

  3. $\text{mg}$

  4. $\frac{1}{2}\text{m}\omega^2\text{l}$

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Q 4M.C.Q (1 Marks)1 Mark
A circular disc A of radius r is made from an iron plate of thickness (t) and another circular disc B of radius 4r is made from an iron plate of thickness $\frac{\text{t}}{4}.$ The relation between the moments of inertia IA and IB is:
  1. IA > IB
  2. IA = IB
  3. IA < IB
  4. Depends on the actual values of t and r.
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Q 5M.C.Q (1 Marks)1 Mark
A sphere can roll on a surface inclined at an angle $\theta$ if the friction coefficient is more than $\frac{2}{7}\text{g}\tan \theta.$ Suppose the friction coefficient is $\frac{1}{7}\text{g}\tan \theta.$ If a sphere is released from rest on the incline:
  1. It will stay at rest.
  2. It will make pure translational motion.
  3. It will translate and rotate about the centre.
  4. The angular momentum of the sphere about its centre will remain constant.
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Q 61 Marks Question1 Mark
In a rotating body, $\text{a}=\alpha\text{r}$ and $\text{v}=\omega\text{r}.$ Thus $\frac{\text{a}}{\alpha}=\frac{\text{v}}{\omega}.$ Can a co you use the theorems of ratio and proportion studied in algebra so as to write

$\frac{\text{a}+\alpha}{\text{a}-\alpha}=\frac{\text{v}+\omega}{\text{v}-\omega}$

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Q 71 Marks Question1 Mark
If the sum of all the forces acting on a body is zero, is it necessarily in equilibrium? If the sum of all the forces on a particle is zero, is it necessarily in equilibrium?
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Q 101 Marks Question1 Mark
When a body is weighed on an ordinary balance we demand that the arm should be horizontal if the weights on the two pans are equal. Suppose equal weights are put on the two pans, the arm is kept at an angle with the horizontal and released. Is the torque of the two weights about the middle point (point of support) zero? Is the total torque zero? If so, why does the arm rotate and finally become horizontal?
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Q 122 Marks Questions2 Marks
A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100rev/sec in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
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Q 132 Marks Questions2 Marks
The torque of a force $\overrightarrow{\text{F}}$ about a point is defined as $\overrightarrow{\text{r}}=\overrightarrow{\text{r}}\times\overrightarrow{\text{F}}.$ Suppose $\overrightarrow{\text{r}}, \overrightarrow{\text{F}}$and $\overrightarrow{\text{r}}$ are all nonzero. Is $\text{r}\times\overrightarrow{\text{r}}\Bigg|\Bigg|\overrightarrow{\text{F}}$ always true? Is it ever true?
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Q 142 Marks Questions2 Marks
A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?
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Q 152 Marks Questions2 Marks
A solid sphere of mass m is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup.
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Q 163 Marks Question3 Marks
A solid sphere is set into motion on a rough horizontal surface with a linear speed v in the forward direction and an angular speed $\frac{\text{v}}{\text{R}}$ in the anticlockwise direction as shown in figure. Find the linear speed of the sphere:
  1. When it stops rotating.
  2. When slipping finally ceases and pure rolling starts.

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Q 173 Marks Question3 Marks
Two particles of masses m1 and m2 are joined by a light rigid rod of length r. The system rotates at an angular speed co about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is $\text{L}=\mu\text{r}^2\omega$ where $\mu$ is the reduced mass of the system defined as $\mu=\frac{\text{m}_1\text{m}_2}{\text{m}_1+\text{m}_2}.$
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Q 183 Marks Question3 Marks
A simple pendulum of length (l) is pulled aside to make an angle $\theta$ with the vertical. Find the magnitude of the torque of the weight (w) of the bob about the point of suspension. When is the torque zero?
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Q 193 Marks Question3 Marks
A dumb-bell consists of two identical small balls of mass $\frac{1}{2}\text{kg}$ each connected to the two ends of a 50cm long light rod. The dumb-bell is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of 10rad/s. An impulsive force of average magnitude 5.0N acts on one of the masses in the direction of its velocity for 0.10s. Find the new angular velocity of the system.
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Q 203 Marks Question3 Marks
A cubical block of mass m and edge a slides down a rough inclined plane of inclination $\theta$ with a uniform speed. Find the torque of the normal force acting on the block about its centre.
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Q 214 Marks Question4 Marks
A kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I. The system is at rest when a friend throws a ball of mass m and the kid catches it. If the velocity of the ball is v horizontally along the tangent to the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.
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Q 224 Marks Question4 Marks
The moon rotates about the earth in such a way that only one hemisphere of the moon faces the earth. Can we ever see the ''other face'' of the moon from the earth? Can a person on the moon ever see all the faces of the earth?

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Q 234 Marks Question4 Marks
A ladder is resting with one end on a vertical wall and the other end on a horizontal floor. Is it more likely to slip when a man stands near the bottom or near the top?
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Q 265 Marks Questions5 Marks
A uniform rod of length L rests against a smooth roller as shown in figure. Find the friction coefficient between the ground and the lower end if the minimum angle that the rod can make with the horizontal is $\theta.$

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Q 275 Marks Questions5 Marks
A uniform rod of length L lies on a smooth horizontal table. A particle moving on the table strikes the rod perpendicularly at an end and stops. Find the distance travelled by the centre of the rod by the time it turns through a right angle. Show that if the mass of the rod is four times that of the particle, the collision is elastic.
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Q 285 Marks Questions5 Marks
A uniform wheel of radius R is set into rotation about its axis at an angular speed $\omega.$ This rotating wheel is now placed on a rough horizontal surface with its axis horizontal. Because of friction at the contact, the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling on the surface. Find the linear speed of the wheel after it starts pure rolling.
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Q 295 Marks Questions5 Marks
The pulley shown in figure has a radius 10cm and moment of inertia 0.5kg-m2 about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4.0kg block.

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Q 305 Marks Questions5 Marks
Two blocks of masses 400g and 200g are connected through a light string going over a pulley which is free to rotate about its axis. The pulley has a moment of inertia 1.6 x 10-4kg-m2 and a radius 2.0cm. Find:
  1. The kinetic energy of the system as the 400g block falls through 50cm.
  2. The speed of the blocks at this instant.
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