Advertisements
Advertisements
Question
The acceleration due to gravity on the surface of moon is 1.7 ms–2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms–2)
Advertisements
Solution 1
Acceleration due to gravity on the surface of moon, g' = 1.7 m s–2
Acceleration due to gravity on the surface of earth, g = 9.8 m s–2
Time period of a simple pendulum on earth, T = 3.5 s
`T = 2pisqrt(1/g)`
Where l is the length of the pendulum
`:.l = T^2/(2pi)^2 xx g`
`=(3.5)^2/(4xx(3.14)^2) xx 9.8 m`
The length of the pendulum remains constant.
On moon’s surface, time period, `T' = 2pi sqrt(1/g^')`
`= 2pi sqrt(((3.5)^2/(4xx3.14)^2 xx 9.8)/1.7) = 8.4 s`
Hence, the time period of the simple pendulum on the surface of moon is 8.4 s.
Solution 2
Here `g_m = 1.7 ms^(-2), g_e= 9.8 ms^2; T_m = ? T_e= 3.5 s^(-1)`
Since `T_e = 2pi sqrt(1/(g_e))` and `T_m = 2pisqrt(1/g_m)`
`:. T_m/T_e = sqrt(g_e/g_m) => T_m = T_e = sqrt(g_e/g_m)`
`= 3.5 sqrt(9.8/1.7) = 8.4 s`
Solution 3
Here `g_m = 1.7 ms^(-2), g_e= 9.8 ms^2; T_m = ? T_e= 3.5 s^(-1)`
Since `T_e = 2pi sqrt(1/(g_e))` and `T_m = 2pisqrt(1/g_m)`
`:. T_m/T_e = sqrt(g_e/g_m) => T_m = T_e = sqrt(g_e/g_m)`
`= 3.5 sqrt(9.8/1.7) = 8.4 s`
RELATED QUESTIONS
If the metal bob of a simple pendulum is replaced by a wooden bob of the same size, then its time period will.....................
- increase
- remain same
- decrease
- first increase and then decrease.
The phase difference between displacement and acceleration of a particle performing S.H.M. is _______.
(A) `pi/2rad`
(B) π rad
(C) 2π rad
(D)`(3pi)/2rad`
Answer the following questions:
A time period of a particle in SHM depends on the force constant k and mass m of the particle: `T = 2pi sqrt(m/k)` A simple pendulum executes SHM approximately. Why then is the time
Answer the following questions:
What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?
The cylindrical piece of the cork of density of base area A and height h floats in a liquid of density `rho_1`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period
`T = 2pi sqrt((hrho)/(rho_1g)`
where ρ is the density of cork. (Ignore damping due to viscosity of the liquid).
A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x0 and v0. [Hint: Start with the equation x = acos (ωt+θ) and note that the initial velocity is negative.]
Define practical simple pendulum
Show that, under certain conditions, simple pendulum performs the linear simple harmonic motion.
The period of oscillation of a simple pendulum of constant length at the surface of the earth is T. Its time period inside mine will be ______.
A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is ______.
Which of the following statements is/are true for a simple harmonic oscillator?
- Force acting is directly proportional to displacement from the mean position and opposite to it.
- Motion is periodic.
- Acceleration of the oscillator is constant.
- The velocity is periodic.
The length of a second’s pendulum on the surface of earth is 1 m. What will be the length of a second’s pendulum on the moon?
A body of mass m is situated in a potential field U(x) = U0 (1 – cos αx) when U0 and α are constants. Find the time period of small oscillations.
Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2° to the right with the vertical, the other pendulum makes an angle of 1° to the left of the vertical. What is the phase difference between the pendulums?
A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute S.H.M. with a time period. `T = 2πsqrt(m/(Apg))` where m is mass of the body and ρ is density of the liquid.
In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be:
If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is `x/2` times its original time period. Then the value of x is ______.
