Relating Circular Motion to SHM

Q.

The velocity v of a particle at time t is given by v=at+b\t+c where a, b, c are constants . What will be the dimensions of a, b and c

Q. A body is moving with velocity 30m/s towards east. After 10 seconds its velocity becomes 40m/s towards north. The average acceleration of the body is



(Answer coming is 5m/S2)

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.

What is SHM in Physics?

Q.

What is u in Physics?

Q. If the apparent value of dip at a place in two perpendicular vertical planes are respectively ${30}^{\circ }$ and ${45}^{\circ }$, then the true angle of dip at that place is

1. ${\cot }^{-1}\left(2\right)$
2. ${\tan }^{-1}\left(2\right)$
3. ${\cot }^{-1}\left(\sqrt{3}\right)$
4. ${\cot }^{-1}\left(\sqrt{5}\right)$

Q. A block having mass $m$ and charge $q$ is connected by a spring of force constant $k$. The block lies on a frictionless horizontal track and a uniform electric field $E$ acts on system as shown. The block is relased from rest when the spring is unstretched $(atx=0)$. Identify the wrong statement.

1. Amplitude of the oscillation of block is $\frac{qE}{k}$
2. Amplitude of the oscillation is $\frac{2qE}{k}$
3. maximum extension in the spring is $\frac{2qE}{k}$
4. In equilibrium position extension in the spring is $\frac{qE}{k}$

Q.

what does |dv/dt| and d|v|/dt represent . Can these be equal.

Q. A body is moving with a uniform acceleration. Its velocity after 5 seconds is 25m/s and after 8 seconds is 34m/s. Calculate the distance it will cover in the 10th second.

Q.

A block of mass $1\mathrm{Kg}$ attached to a spring is made to oscillate with an initial amplitude of $12\mathrm{cm}$. After $2$ minutes the amplitude decreases to $6\mathrm{cm}$. Determine the value of the damping constant for this motion. (take $\ln \left(2\right)=0.693$).

1. $3.3\times {10}^2{\mathrm{kgs}}^{-1}$

2. $5.7\times {10}^{-3}\mathrm{Kg}{s}^{-1}$

3. $1.16\times {10}^{-2}{\mathrm{Kgs}}^{-1}$

4. $0.69\times {10}^2{\mathrm{Kgs}}^{-1}$

Q. What is damped oscillations

Q. The oscillation of body on a smooth horizontal surface is represented by the equation,
$x=A\cos \left(\omega t\right)$
Where
$x=$ displacement at time $t$
$\omega =$ frequency of oscillation
Which one of the following graphs shows correctly the variation ${}^{\prime }{a}^{\prime }$ with ${}^{\prime }{t}^{\prime }$?

1. 
2. 
3. 
4. 

Q.

A student is standing at a distance of 50 m from the bus as soon as the bus begins its motion with an acceleration of 1 M per second the stuudent starts running towards the Bus with uniform velocity U asuming the motion to be along straight road the minimum value of u so that the student is able to catch the bus is

Q.

What is the principle of compound pendulum?

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

Q.

Is inverse $\sin$ the same as $cosec$?

Q.

What is damped SHM?

Q.

An object starts from rest with constant acceleration of 4 m/s^2 find the distance travelled by that object in 5th half second

Q.

A body is in motion along a straight line. As it crosses a fixed point a stop watch is started. The body travels a distance of 1.80m in the first 3 second and 2.20m in next 5 seconds what will be the velocity at the end of 9 seconds?

Q. What is dv/ds? How can it used

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.

What affects the swing rate of a pendulum?

Q.

If Y = A Sin ( wt- kx ) find dimension of w and k if Y is displacement, x is distance and t is time.

Q.

A train is running at full speed when brakes are applied. In the first minute it travels 8 km and in the next minute it travels 3 km. initial speed of the train is

Q. Why is it easier to balance a bicycle in motion?

Q.

A body covers 200cm in the first 2sec and 220cm in next 4sec under constant acceleration then velocity of body after 7sec is?

Q.

The relation between time and displacement of a moving object is given as t= ax² + bx, where a, b are constants. Prove that the acceleration of the body is( -2av³)

Q.

Check the correctness

$s=u+\frac{1}{2}a(2t-1)$