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While driving around a curve of 200 m radius the driver noted that pendulum in the car hangs at an angle of $15^{0}$ to the vertical. The speedometer of the car reads $(i n m s^{- 1})$

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Important Questions on Simple Harmonic Motion

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

A cylindrical plastic bottle of negligible mass is filled with

310 ml

of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency

ω .

If the radius of the bottle is

2 .5 cm

then

ω

is close to:

(

density of water

= 10^{3} kg m^{- 3})

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

Two light identical springs of spring constant

k

are attached horizontally at the two ends of a uniform horizontal rod

A B

of length

l

and mass

m .

The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:
Question Image

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

Two masses

m

and

\frac{m}{2}

are connected at the two ends of a massless rigid rod of length

l .

The rod is suspended by a thin wire of torsional constant

k

at the centre of mass of the rod-mass system (see figure). Because of torsional constant

k,

the restoring torque is

τ = k θ

for angular displacement

θ .

If the rod is rotated by

θ_{0}

and released, the tension in it when it passes through its mean position will be:
Question Image

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

Naturally oscillating systems undergo

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

A rod of mass

M

and length

2 L

is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass

m

, are attached at a distance

L / 2

from its centre on both sides, it reduces the oscillation frequency by

20 %

. The value of ratio

m / M

is close to

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

What is the time period of the pendulum in a lift, which is falling freely under gravity

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

A car is moving on a plane inclined at

30 °

to the horizontal with an acceleration of

10 {m s}^{- 2}

parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take

g = 10 {m s}^{- 2}

)

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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:

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

A cylindrical block of wood of mass

10 kg

and radius

10 cm

is floating in water with its axis vertical. When it is depressed a little and then released, it starts executing simple hormonic motion (SHM). The frequency of the SHM, executed by the block is:
(Assume

g = 10 m s^{- 2}

and let

ρ

is the density of the water)

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

The time period of oscillation of a simple pendulum of length

L

suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination

α

, is given by :

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

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,

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Simple Pendulum

A rectangular block of mass

m

and area of cross-section

A

floats in a liquid of density

ρ

. If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period

T

. Then

While driving around a curve of 200 m radius the driver noted that pendulum in the car hangs at an angle of 150 to the vertical. The speedometer of the car reads (in ms-1)

Important Questions on Simple Harmonic Motion

Learn and Prepare for any exam you want !

While driving around a curve of 200 m radius the driver noted that pendulum in the car hangs at an angle of $15^{0}$ to the vertical. The speedometer of the car reads $(i n m s^{- 1})$