Question 1 :
A pendulum is suspended from the roof of a rail road car. When the car is moving on a circular track the pendulum inclines.
Question 3 :
A stone of mass $0.25 kg$ tied to the end of a string is whirled round in a circle of radius $1.5 m$ with speed $40 { rev }/{ min }$ in a horizontal plane. What is the tension in the string and what is the maximum speed with which the stone can be whirled around, if the string can withstand a maximum tension of $200 N$?
Question 4 :
A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are $\vec{a} = 2\vec{i} + 3\vec{j} \ m/s^2$ and $\vec{P} = 6\vec{i} - 4\vec{j}$ kgm/s. Then the motion of the particle is:
Question 5 :
A car runs at constant speed on a circular track of radius 100 m taking 62.8 s on each lap. What is the average speed and average velocity on each complete lap? $(\pi\, =\, 3.14)$
Question 6 :
The real force 'F' acting on a particle of mass 'm' performing circular motion acts along the radius of circle 'r' and is directed towards the centre of circle. The square root of magnitude of such force is? (T$=$ periodic time)
Question 7 :
Two coins are sitting on a horizontal disk, which is rotating at a constant speed.<br>One coin is a penny located halfway between the center of the disk the edge. The other coin is a dime located at the edge of the disk.<br>How does the magnitude of the dime's acceleration compare to the magnitude of the penny's acceleration?
Question 8 :
Assertion: Velocity and acceleration of a particle in circular motion at some instant are: $\displaystyle \vec{v}= \left ( 2\hat{i} \right )ms^{-1}\:and\:\vec{a}= \left ( -\hat{i}+2\hat{j} \right )ms^{-2},$ then radius of circle is $2$ m.
Reason: Speed of particle is decreasing at a rate of $1\displaystyle ms^{-2}.$
Question 9 :
The linear and angular acceleration of a particle are $10\ m/sec^2$ and $5\ rad/sec^2$ respectively, it will be at a distance of ___ m from the axis of rotation
Question 10 :
A particle moves with constant angular velocity in a circle. During the motion its
Question 11 :
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first two seconds it rotates through angle $\theta_1$. In the next two seconds it rotates through angle $\theta_2$. What is the ratio $\theta_2 / \theta_1$?<br>
Question 12 :
<span>Find out the </span><span>angular acceleration of a</span><span> washing machine, starting from rest, accelerates within $3.14 s$ to a point where it is revolving at a frequency of $2.00 Hz$.</span>
Question 13 :
A string of length $ \ell $ has one end fixed and a particle of mass m is attached to the other end. If the particle describe a horizontal circle at an angular speed $ \omega $, in gravity free space.
Question 14 :
Assertion: the velocity of a body at the bottom of an inclined plan e of a given height is more when it slides down the plane compared to when it is rolling down the same plane
Reason: In rolling down , a body acquires both kinetic energy of translation and rotation
Question 15 :
A particle starts travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment when particle complete half the circular track, is:
Question 16 :
A disc is rotating in a room. A boy standing near the rim of the disc of radius $R$ finds the water droplet falling from the ceiling is always falling on his head. As one drop hits his head, other one starts from the ceiling. If height of the roof above his head is $H$, then angular velocity of the disc is
Question 17 :
When a body moves with a constant speed along a circle:
Question 18 :
A shaft initially rotating at $1725$ rpm is brought to rest uniformly in $20s.$ The number of revolutions that the shaft will make during this time is<br><br>
Question 19 :
A fan is running at $3000\ rpm$. It is switched off. It comes to rest by uniformly decreasing its angular speed in $10\ seconds$. The total number of revolutions in this period.
Question 20 :
<span> A mass is attached to the end of a string of which is tied to a fixed point O. The mass is released from the initial horizontal position of the string. Below the point O at what minimum distance a peg P be should fixed so that the mass tums about P and can describe a complete circle in the vertical plane?</span>
Question 21 :
A cyclist turns a corner with a radius of 50 m at a speed of 20 m/s . What is the magnitude of the cyclist's acceleration?
Question 22 :
If a particle is rotating with an angular velocity $\omega$ and angular acceleration $\alpha$, then ,
Question 23 :
The driver of a car travelling at velocity $v$ suddenly see a broad wall in front of him at a distance $d$. He should :
Question 24 :
A stone tied to the end of a string $80\;cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $22\;s$ then the acceleration of the stone is :
Question 25 :
A particle moving at a circle. If at an instant its linear velocity vector, angular velocity and position vector are $\overline { v } , \overline { \omega }$ and $\vec { r }$ respectively then, the correct option is<br/>
