Relating Circular Motion to SHM

Q. A particle moves in a circular path with a continuously increasing speed. Its motion is

1. periodic

2. oscillatory

3. simple harmonic

4. none of them

Q. A particle moves in a circular path with a uniform speed. Its motion is

1. periodic

2. oscillatory

3. simple harmonic

4. angular simple harmonic

Q.

The displacement of a particle is given by $\overrightarrow{r}=A(\overrightarrow{i}cos\omega t+\overrightarrow{j}sin\omega t)$The motion of the particle is

1. simple harmonic

2. on a straight line

3. on a circle

4. with constant acceleration

Q. A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is

1. periodic

2. oscillatory

3. angular simple harmonic

4. simple harmonic

Q. The radius of circle, period of revolution, initial position and sense of revolution are indicated in the figure.


The y-projection of the radius vector of the rotating particle $P$ is

1. $y\left(t\right)=-3\cos 2\pi t$, where $y$ is in $m$
2. $y\left(t\right)=4\sin \left(\frac{\pi t}{2}\right)$, where $y$ is in $m$
3. $y\left(t\right)=3\cos \left(\frac{\pi t}{2}\right)$, where $y$ is in $m$
4. $y\left(t\right)=3\cos \left(\frac{3\pi t}{2}\right)$, where $y$ is in $m$

Q. The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure.

y - projection of the radius vector of rotating particle P is

1. $y\left(t\right)=3cos\left(\frac{3\pi t}{2}\right),$ where y is in $m$
2. $y\left(t\right)=-3cos2\pi t,$ where y is in $m$
3. $y\left(t\right)=4sin\left(\frac{\pi t}{2}\right),$ where y is in $m$
4. 
   $y\left(t\right)=3cos\left(\frac{\pi t}{2}\right),$ where y is in $m$

Q. Average velocity of a particle executing S.H.M. in one complete vibration is

1. $\frac{A{\omega }^2}{2}$
2. $\frac{A\omega }{2}$
3. $A\omega$
4. zero

Q. A body of mass $0.01\text{kg}$ executes simple harmonic motion (SHM) about $x=0$ under the influence of a force $F$ which varies with $x$ as shown in figure. Find the time period of SHM of the body.

1. $\frac{\pi }{10}$
2. $\frac{3\pi }{10}$
3. $\frac{\pi }{5}$
4. $\frac{\pi }{3}$

Q. Two particles are in SHM in a straight line about same equilibrium position. Amplitude $A$ and time period $T$ of both the particles are equal. At time $t=0$, one particle is at displacement $y_1=+A$ and the other at $y_2=-\frac{A}{2}$, and they are approaching towards each other. After what time they cross each other?

1. $\frac{T}{3}$
2. $\frac{5T}{6}$
3. $\frac{T}{6}$
4. $\frac{T}{4}$

Q. Two simple harmonic motions given by $x=A\sin (\omega t+\delta )$ and $y=A\sin (\omega t+\delta +\frac{\pi }{2})$ act on a particle simultaneously. Then the motion of particle will be:

1. circular anti-clockwise
2. elliptical clockwise
3. elliptical anti-clockwise
4. circular clockwise