A simple pendulum was designed on a day when the room temperature was 22 ° C . On a hot summer day when the temperature rise to 50 ° C , the length of pendulum increased by a fraction 1 10 . What would be the period of the second's pendulum on that day? What will be the effect on the time of a clock having that pendulum on that day?

Time period of a simple pendulum is given by T = 2 π l g . Time period of second's pendulum is 2 s . If due to change in the length the time period becomes T ' , then T ' T = L ' L ⇒ T ' = 2 × 1 + 1 10 10 ≃ 2 × 1 . 05 = 2 . 1 s Therefore, time period of second's pendulum will be 2 . 1 s on that day. And, the clock will be slower on that day.

A simple pendulum was designed on a day when the room temperature was 22 ° C . On a hot summer day when the temperature rise to 50 ° C , the length of pendulum increased by a fraction 1 10 . What would be the period of the second's pendulum on that day? What will be the effect on the time of a clock having that pendulum on that day?

Time period of a simple pendulum is given by T = 2 π l g . Time period of second's pendulum is 2 s . If due to change in the length the time period becomes T ' , then T ' T = L ' L ⇒ T ' = 2 × 1 + 1 10 10 ≃ 2 × 1 . 05 = 2 . 1 s Therefore, time period of second's pendulum will be 2 . 1 s on that day. And, the clock will be slower on that day.

MEDIUM

Earn 100

A simple pendulum was designed on a day when the room temperature was $22 ° C$ . On a hot summer day when the temperature rise to $50 ° C$ , the length of pendulum increased by a fraction $(\frac{1}{10})$ . What would be the period of the second's pendulum on that day? What will be the effect on the time of a clock having that pendulum on that day?

Important Questions on Oscillations

HARD

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

A pendulum has length of

0.4 m

and maximum speed

4 m s^{- 1}

. When the length makes an angle

30 °

with the horizontal, its speed will be

[\sin \frac{π}{6} = \cos \frac{π}{3} = 0.5

and

g = 10 m s^{- 2}]

MEDIUM

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

Two simple pendulums of lengths

5 m

and

20 m

respectively are given small displacement in one direction at the same time they will again be in the same sense when the pendulum of shorter length has completed

n

oscillations. Then,

n

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

Two clocks

A

and

B

are synchronized to show the same time on earth. Clock

A

is based on oscillations of spring and clock

B

is based on a pendulum motion. If these two clocks are taken to the surface of the moon, then

MEDIUM

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

If the time period of a two meter long simple pendulum is

2 s

, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

In an experiment to determine the gravitational acceleration

g

of a place with the help of a simple pendulum, the measured time period squared is plotted against the string length of the pendulum in the figure. What is the value of

g

at the place?

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

A simple pendulum has time period $T_{1}$ . The point of suspension is now moved upward according to the relation $y = k t^{2}, (k = 1 m s^{- 2})$ where $y$ is the vertical displacement. The time
period now becomes $T_{2}$ .

The ratio of $\frac{T_{1}^{2}}{T_{2}^{2}} (g = 10 m s^{- 2})$ is

MEDIUM

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

The time period of a bob performing simple harmonic motion in water is

2 s

. If density of bob is

\frac{4}{3} \times 10^{3} kg m^{- 3}

, then time period of bob performing simple harmonic motion in air will be

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

The time period of a simple pendulum inside a stationary lift is

T

. If the lift starts moving upwards with an acceleration of

\frac{g}{3}

, its time period will be,

MEDIUM

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

A simple pendulum oscillating in air has period

T

. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is

\frac{1}{16} t h

of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

HARD

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulum is

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

Given below are two statements:
Statement $I$ : A second's pendulum has a time period of $1$ second.

Statement $II$ : It takes precisely one second to move between the two extreme positions. In the light of the above statements,

choose the correct answer from the options given below

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

A tunnel is dug along the diameter of the earth. A mass

m

is dropped into it. How much time does it take to cross the earth?

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

The length of the seconds pendulum is

1 m

on earth. If the mass and diameter of the planet is

1.5

times that of the earth, the length of the seconds pendulum on the planet will be nearly

HARD

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

The bob of a swinging second pendulum (one whose time period is

2 s

) has a small speed

v_{0}

at its lowest point. Its height from this lowest point

2.25 s

after passing through it, is given by

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

Time period of a simple pendulum is

T

inside a lift when the lift is stationary. If the lift moves upwards with an acceleration

\frac{g}{2}

, the time period of pendulum will be :

MEDIUM

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

Two simple pendulums of lengths in the ratio

4 : 1

start oscillating at

t = 0

. They will again be in phase after the shorter pendulum has made

n

oscillations. Find the value of

n

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

T_{0}

is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to

\frac{1}{16}

times of its initial value, the modified time period is

EASY

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

The bob of simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob get suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

MEDIUM

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

In an experiment to determine the period of a simple pendulum of length

1 m

, it is attached to different spherical bobs of radii

r_{1}

and

r_{2}

. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be

5 \times 10^{- 4} s

, the difference in radii,

|r_{1} - r_{2}|

is best-given by

HARD

Physics>Oscillation and Wave>Oscillations>Simple Harmonic Motion

The path length of oscillation of simple pendulum of length

1 m

16 cm

. Its maximum velocity is

(g = π^{2} {m s}^{-2})

Important Questions on Oscillations

Learn and Prepare for any exam you want !