Advertisements
Advertisements
प्रश्न
A simple pendulum is constructed by hanging a heavy ball by a 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second? (b) What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is 1.67 m/s2?
Advertisements
उत्तर
It is given that:
Length of the pendulum, l = 5 m
Acceleration due to gravity, g = 9.8 ms-2
Acceleration due to gravity at the moon, g' = 1.67 ms-2
(a) Time period \[\left( T \right)\] is given by,
\[T = 2\pi\sqrt{\frac{l}{g}}\]
\[= 2\pi\sqrt{\frac{5}{9 . 8}}\]
\[ = 2\pi\sqrt{0 . 510} = 2\pi \left( 0 . 71 \right) s\]
i.e. the body will take 2 \[\pi\](0.7) seconds to complete an oscillation.
Now, frequency \[\left( f \right)\]is given by,
\[f = \frac{1}{T}\]
\[\therefore f = \frac{1}{2\pi\left( 0 . 71 \right)} \]
\[ = \frac{0 . 70}{\pi} Hz\]
(b) Let
\[g'\] be the value of acceleration due to gravity at moon. Time period of simple pendulum at moon \[\left( T' \right)\],is given as:
\[T' = 2\pi\sqrt{\left( \frac{l}{g'} \right)}\]
On substituting the respective values in the above formula, we get:
\[ = \frac{1}{2\pi}\sqrt{\frac{1 . 67}{5}} = \frac{1}{2\pi}\left( 0 . 577 \right)\]
\[ = \frac{1}{2\pi\sqrt{3}} Hz\]
APPEARS IN
संबंधित प्रश्न
Define phase of S.H.M.
A particle executes simple harmonic motion. If you are told that its velocity at this instant is zero, can you say what is its displacement? If you are told that its velocity at this instant is maximum, can you say what is its displacement?
A hollow sphere filled with water is used as the bob of a pendulum. Assume that the equation for simple pendulum is valid with the distance between the point of suspension and centre of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?
The motion of a particle is given by x = A sin ωt + B cos ωt. The motion of the particle is
The displacement of a particle is given by \[\overrightarrow{r} = A\left( \overrightarrow{i} \cos\omega t + \overrightarrow{j} \sin\omega t \right) .\] The motion of the particle is
Which of the following quantities are always positive in a simple harmonic motion?
Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel. The motion of the particle as seen from the earth is
(a) simple harmonic
(b) parabolic
(c) on a straight line
(d) periodic
The angle made by the string of a simple pendulum with the vertical depends on time as \[\theta = \frac{\pi}{90} \sin \left[ \left( \pi s^{- 1} \right)t \right]\] .Find the length of the pendulum if g = π2 m2.
The pendulum of a certain clock has time period 2.04 s. How fast or slow does the clock run during 24 hours?
A small block oscillates back and forth on a smooth concave surface of radius R in Figure. Find the time period of small oscillation.
A spherical ball of mass m and radius r rolls without slipping on a rough concave surface of large radius R. It makes small oscillations about the lowest point. Find the time period.
A simple pendulum fixed in a car has a time period of 4 seconds when the car is moving uniformly on a horizontal road. When the accelerator is pressed, the time period changes to 3.99 seconds. Making an approximate analysis, find the acceleration of the car.
A closed circular wire hung on a nail in a wall undergoes small oscillations of amplitude 20 and time period 2 s. Find (a) the radius of the circular wire, (b) the speed of the particle farthest away from the point of suspension as it goes through its mean position, (c) the acceleration of this particle as it goes through its mean position and (d) the acceleration of this particle when it is at an extreme position. Take g = π2 m/s2.
Three simple harmonic motions of equal amplitude A and equal time periods in the same direction combine. The phase of the second motion is 60° ahead of the first and the phase of the third motion is 60° ahead of the second. Find the amplitude of the resultant motion.
A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of 45° with the X-axis. The two motions are given by x = x0 sin ωt and s = s0 sin ωt. Find the amplitude of the resultant motion.
The length of a second’s pendulum on the surface of the Earth is 0.9 m. The length of the same pendulum on the surface of planet X such that the acceleration of the planet X is n times greater than the Earth is
A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is
Define the frequency of simple harmonic motion.
The displacement of a particle is represented by the equation y = sin3ωt. The motion is ______.
A container consist of hemispherical shell of radius 'r ' and cylindrical shell of height 'h' radius of same material and thickness. The maximum value h/r so that container remain stable equilibrium in the position shown (neglect friction) is ______.
