Pure Rotation about an Axis

Q.

How many types of motion does the Earth have?

Q.

For a body in pure rolling, its rotational kinetic energy is $\frac{1}{2}$ times of its translational kinetic energy. The body should be?

1. Solid cylinder

2. Ring

3. Solid sphere

4. Hollow sphere

Q. A uniform disc of mass $M$ and radius $R$ is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc as shown in figure below. If we hang a body of mass $m$ with the cord, it has acceleration $a$ as shown in figure. Find the angular acceleration of the disc $\left(\alpha \right)$.

1. $\frac{2m(a+g)}{MR}$
2. $\frac{2M(a+g)}{mR}$
3. $\frac{2M(g-a)}{mR}$
4. $\frac{2m(g-a)}{MR}$

Q. Motion of a rigid body which takes place in such a way that all of its particles move in a circle about a fixed axis with common angular velocity. Type of motion of rigid body is

1. Pure translational motion
2. Pure rotational motion
3. Combined translational and rotational motion
4. None of these

Q.

A body rotates about a fixed axis with an angular acceleration of one radian/second/second. Through what angle does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s.

Q.

A wheel of radius $R$ and mass $M$ is placed at the bottom of a fixed step of height $R$ as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $\tau$ about an axis normal to the plane of the paper passing through the point $Q$. Which of the following options is/are correct?

1. If the force is applied tangentially at point $S$ then $\tau \ne 0$ but the wheel never climbs the step

2. If the force is applied normal to the circumference at point P then $\tau$ is zero

3. If the force is applied normal to the circumference at point X then $\tau$ is constant

4. If the force is applied at point P tangentially then $\tau$ decreases continuously as the wheel climbs

Q. A rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:

1. $\frac{g}{13l}$
2. $\frac{g}{3l}$
3. $\frac{g}{2l}$
4. $\frac{7g}{3l}$

Q. Assertion :A hollow shaft is found to be stronger than a solid shaft made of same material. Reason: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

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.

Find out torque about points $A$, $O$ and $B$ if $\overrightarrow{F}$ = $10\hat{i}$

1. 

2. 

3. 

4. 

Q. A boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give explanation to support your diagram.

Q. When does a body rotate? State one way to change the direction of rotation of the body .Give a suitable example

Q. A uniform rod of mass 𝑚 and length $l_0$ is rotating with a constant angular speed $\omega$ about a vertical axis passing through its point of suspension. The moment of inertia of the rod about the axis of rotation if it makes an angle $\theta$ to the vertical (axis of rotation) is

1. $\frac{2m{l}_0^2{\sin }^2\theta }{3}$
2. $\frac{m{l}_0^2{\sin }^2\theta }{3}$
3. $\frac{m{l}_0^2{\sin }^2\theta }{12}$
4. $\frac{m{l}_0^2{\sin }^2\theta }{6}$

Q. The locus of the centers of all the circular motion of the particles present in the rotating body is known as

1. Axis of translation
2. Axis of rotation
3. Center of mass
4. None of these

Q.

What is rotatory motion , give some examples.

Q. A uniform rod of length $\frac{6}{10}\text{m}$ is suspended from one end such that it is free to rotate about an axis passing through that end and perpendicular to the length. The minimum speed $\text{m/s}$ must be imparted to the lower end so that the rod completes one full revolution, is (Integer only)

Q.

Which one is an example of a uniform motion?

1. A freely falling stone.

2. A stone projected vertically upward.

3. Earth turning around its axis.

4. A bicycle driven on crowded Road.

Q. A ring is hung on a nail. It can oscillate, without slipping or sliding $\left(i\right)$ in its plane with a time period $T_1$ and $\left(ii\right)$ back and forth in a direction perpendicular to its plane, with a period $T_2$. The ratio $\frac{T_1}{T_2}$ will be

1. $\frac{2}{\sqrt{3}}$
2. $\frac{2}{3}$
3. $\frac{3}{\sqrt{2}}$
4. $\frac{\sqrt{2}}{3}$

Q.

The motion of spinning top and giant wheel is an example of _________ motion​.

Q. Motion is relative or absolute

Q.

A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction = $\mu )$ with speed of centre u, as shown in the figure. It collides with a smooth vertical wall, the coefficient of restitution being ½. Choose the correct options.

1. Speed of C.O.M just after collision is $\frac{u}{2}$.

2. Friction acts rightward just after collision

3. Angular velocity does not change during collision

4. The speed of the centre of the sphere when it begins pure rolling does not depend on $\mu$.

Q. 220V, 10 kW, 900 rpm separately excited DC motor has an armature resistance $R_a=0.02\Omega$ When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by motor is 70 N - m. Neglecting the rotational losses of the machine, the current drawn by the motor from 220 V supply is

1. 30 A
2. 34.2 A
3. 22 A
4. 6.95 A

Q.

Classify the piston of a car engine into translatory, rotatory, and oscillatory motion.

Q.

Motion of a potter’s wheel is an example of _________ motion.

Q. Find the dimensions of
(a) angular speed $\omega$
(b) angular acceleration $\alpha$,
(c) torque $\Gamma$ and
(d) moment of inertia $I$

Q.

Object moved to and fro about its mean position, what type of motion does it posses?

Q.

A dice thrown by an athlete is an example of ___________ motion.

Q. A uniform disc of mass M and radius R is mounted on an axle supported in friction less bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. The angular acceleration of the disc is:

1. $\frac{MR}{2T}$
2. $\frac{2T}{MR}$
3. $\frac{T}{MR}$
4. $\frac{MR}{T}$

Q. The locus of the centers of all the circular motion of the particles present in the rotating body is known as

1. Axis of translation
2. Axis of rotation
3. Center of mass
4. None of these

Q. A constant torque of $1000Nm$ turns a wheel of moment of inertia $200kg{m}^2$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $3s$ is :

1. $15rad{s}^{-1}$
2. $0.6rad{s}^{-1}$
3. $6000rad{s}^{-1}$
4. $5rad{s}^{-1}$

Q. Motion of Chakra is Rotary motion

1. True
2. False