Time Period

Q. The angular speed of truck wheel is increased from $900\text{rpm}$ to $2460\text{rpm}$ in $26$ seconds. The number of revolutions by the truck wheel during this time is ______.

$($Assuming the acceleration to be uniform$)$

Q. An athlete completes one round of a circular track of radius 10 m in 40 sec. The distance covered by him in 2 min 20 sec is

1. 140 m
2. 110 m
3. 220 m
4. 70 m

Q. The mean time period of second's pendulum is $2.00s$ and mean absolute error in the time period is $0.05s$. To express maximum estimate of error, the time period should be written as

1. $(2.00\pm 0.025)s$
2. $(2.00\pm 0.10)s$
3. $(2.00\pm 0.05)s$
4. $(2.00\pm 0.01)s$

Q. i) Time for $20$ oscillations of a pendulum is measured as

$t_1=39.6s;t_2=39.9sand{t}_3=39.5s$. What is the precision in the measurements?

ii) Time for $20$ oscillations of a pendulum is measured as
$t_1=39.6s;t_2=39.9sand{t}_3=39.5s$. The precision in the measurements is $0.005s$. What is the accuracy of the measurement?

Q. Two particles $A$ and $B$ are moving in a uniform circular motion in concentric circles of radius $r_A$ and $r_B$ with speed $v_A$ and $v_B$ respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be

1. $r_A:r_B$
2. $v_A:v_B$
3. $r_B:r_A$
4. $1:1$

Q. Two siple pendulums of length $1m$ and $16m$ respectively are both given small displacement in th same direction atthe same instant. They will be again in phase after the shorter pendulum has completed $n$ ascillation. The value of $n$ is

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

Q. As the temperature is increased, the time period of a pendulum:

1. increases as its effective length increases due to shifting of center of mass below the center of the bob.
   
2. decreases as its effective length remains same but the center of mass shifts above the center of the bob
   
3. decreases as its effective length increases even though its center of mass still remains at the center of the bob.
   
4. increases as its effective length increases even though its center of mass still remains at the center of the bob.
   

Q.

A stone of mass $m$ tied to a string of length $l$ is rotating along a circular path with constant speed $v$. What will be the torque on the stone?

Q.

Two racing cars of masses $m_{1}and{m}_2$ are moving in circles of radii $r_{1}and{r}_2$ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

1. $m_1:m_2$

2. $1:1$

3. $r_1:r_2$

4. $m_1{r}_1:m_2{r}_2$

Q. The period of a simple pendulum of length $l\text{is}{T}_1$ and time period of a uniform rod of the same length $l$ pivoted about one end and oscillating in a vertical plane is $T_2$. Amplitude of oscillation in both the cases is small. Then $\frac{T_1}{T_2}$ is

Q.

The angular speed of seconds needle in a mechanical watch is

1. $\frac{\pi }{30}rad/s$

2. $2\pi rad/s$

3. $\pi rad/s$

4. $\frac{60}{\pi }rad/s$

Q. The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of $1.0m$. If the piston moves with simple harmonic motion with an angular frequency of $200rad/min$ , what is its maximum speed?

Q. Find the time period of meeting of the minute hand and second hand of a clock. (Initial positions are shown in the figure below)

1. $\frac{59}{60}\text{min}$
2. $\frac{60}{59}\text{min}$
3. $\frac{3}{4}\text{min}$
4. $\frac{3}{8}\text{min}$

Q. A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90s$, $91s$, $95s$ and $92s$. If the minimum division in the measuring clock is $1s$, then the reported mean time should be

1. $92\pm 5.0s$
2. $92\pm 3s$
3. $92\pm 2s$
4. $92\pm 1.8s$

Q. A simple pendulum hung from the ceiling of a train moving at constant speed has a period $T$. If the train starts acceelrating or decelerating, then what will be effect on time period of pendulumn?

1. Decrease in both casses
2. Decrease only when train accelerates
3. Decrease only when train decelerates
4. Increase in both casses

Q. Two particles revolve concentrically in a horizontal plane in the same direction. The time required to complete one revolution for particle A is 3 min , while for particle B, it is 1 min. The time required for A to complete one revolution relative to B is

1. 2 min
2. 1 min
3. 1.5 min
4. 1.25 min

Q. The phase difference between two displacements at a certain point $A$ at time ${10}^{-3}s$ apart is $\pi$. Find the distance between point $A$ and $B$, which is ${60}^{\circ }$ out of phase than point $A$, if wave velocity is $x$.

1. $1.33\times {10}^{3}x$
2. $0.33\times {10}^{4}x$
3. $2.33\times {10}^{4}x$
4. $3.33\times {10}^{4}x$

Q. A toy car travels in a horizontal circle of radius $2a$. It is kept on the track by a radial elastic string of unstretched length $a$. The period of rotation of the toy car is $T_0$. Now, the toy car is speeded up until it is moving in a circle of radius $3a$. Assuming that the string obeys Hooke's law, find the new period $T$ in terms of $T_0$.

1. $T=T_0$
2. $T=\frac{2T_0}{\sqrt{3}}$
3. $T=\frac{\sqrt{3}}{2}{T}_0$
4. $T=\frac{3}{4}{T}_0$

Q. The length of a simple pendulum is about \(100~cm\) known to an accuracy of \(2~mm\). Its period of oscillation is\( 2~s\) determined by measuring the time for \(500\) oscillations using a clock of \(1~s\) resolution. What is the accuracy (in percentage) in the determined value of \(g\) ?

Q. $A$ cyclist rides a bicycle with a wheel radius of $0.500m$ across campus. $A$ piece of plastic on the front rim makes a clicking sound every time it passes through the fork. If the cyclist counts $320$ clicks between her apartment and the cafeteria, how far has she traveled?

1. $1.5km$
2. $0.80km$
3. $1.0km$
4. $0.50km$

Q. A screw gauge with pitch $1$ mm and $100$ divisions on circular scale is used to measure the thickness of a glass-slab. When there is no object between the studs and the faces of the screw gauge touch each other, the ${40}^{th}$ division of circular scale coincides with the reference line. Now, the glass place is held between the studs and reading of linear scale is found to be$5$ and that of circular scale is $26$. What is the thickness of the glass plate? It is given that zero of linear scale is not visible when the faces touch each other.

Q. The speed of a particle travelling in a circle of radius $20\text{cm}$ increases uniformly from $6\text{m/s}$ to $8\text{m/s}$ in $4\text{sec}$. The angular acceleration of particle is :

1. $5{\text{rad/ s}}^2$
2. $7.5{\text{rad/ s}}^2$
3. $2.5{\text{rad/ s}}^2$
4. $2{\text{rad/ s}}^2$

Q. For a simple pendulum the graph between length and time period will be a

1. straight line
2. hyperbola
3. parabola
4. none of these

Q. Three identical particles $\text{A},\text{B}$ and $\text{C}$ are joined together by a thread as shown in figure. All the particles are moving in a horizontal plane around point $O$. If the velocity of the outermost particle is $v_0$ then the ratio of tensions in the three sections of the string is

1. $3:5:7$
2. $3:4:5$
3. $7:11:6$
4. $3:5:6$

Q. A projectile is fired with a velocity u at right angles to the slope, which is inclined at an angle $\theta$ with the horizontal. Derive an expression for the distance R to the point of impact.

1. $\frac{2V^{2}tan\theta }{gcos\theta }$
2. $\frac{2V^{2}tan\theta }{g}$
3. $\frac{2V^{2}cot\theta }{gcos\theta }$
4. $\frac{2V^{2}tan\theta }{gsin\theta }$

Q. If the distance between the earth and the sun were reduced to half its present value, then the number of days in one year would have been

1. $183$
2. $730$
3. $129$
4. $65$

Q. A person of $80\text{kg}$ mass is standing on the rim of a circular platform of mass $200\text{kg}$ rotating about its axis at $5$ revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre _____.

Q. Find the time period of meeting of the minute hand and second hand of a clock. (Initial positions are shown in the figure below)

1. $\frac{59}{60}\text{min}$
2. $\frac{60}{59}\text{min}$
3. $\frac{3}{4}\text{min}$
4. $\frac{3}{8}\text{min}$

Q. A particle of mass m is moving in a circular path of constant radius 'r' such that its centripetal acceleration $a_c$ is proportional to $t^n$ (where 't' is time ). Then the power 'p' is proportional to

1. $t^n$
2. $t^{n-2}$
3. $t^{n-1}$
4. None of these

Q. For a carrier frequency of $100\text{kHz}$ and a modulating frequency of $5\text{kHz},$ what is the width of AM transmission

1. $5\text{kHz}$
2. $10\text{kHz}$
3. $20\text{kHz}$
4. $200\text{kHz}$