The time period of oscillation of a simple pendulum of length equal to half of the diameter of the earth is about
1. 60 minute
2. 84.6 minute
3. 42.3 minute
4. 24 hour
The time period of the given spring-mass system is:
1. \(2\pi \sqrt{\frac{m}{k}}\)
2. \(2\pi \sqrt{\frac{m}{2k}}\)
3. \(2\pi \sqrt{\frac{2m}{\sqrt{3}k}}\)
4. \(\pi \sqrt{\frac{m}{k}}\)
The equation of simple harmonic motion is given by X = (4 cm), then maximum velocity of the particle in simple harmonic motion is:
1. 25.12 m/s
2. 25.12 cm/s
3. 12.56 m/s
4. 12.56 cm/s
A spring pendulum is on the rotating table. The initial angular velocity of the table is \(\omega_{0}\) and the time period of the pendulum is \(T_{0}.\) Now the angular velocity of the table becomes \(2\omega_{0},\) then the new time period will be:
1. \(2T_{0}\)
2. \(T_0\sqrt{2}\)
3. remains the same
4. \(\frac{T_0}{\sqrt{2}}\)
If the vertical spring-mass system is dipped in a non-viscous liquid, then:
1. | only mean position is changed. |
2. | only the time period is changed. |
3. | time period and mean position both are changed. |
4. | time period and mean position both remain the same. |
The displacement \( x\) of a particle varies with time \(t\) as \(x = A sin\left (\frac{2\pi t}{T} +\frac{\pi}{3} \right)\). The time taken by the particle to reach from \(x = \frac{A}{2} \) to \(x = -\frac{A}{2} \) will be:
1. | \(\frac{T}{2}\) | 2. | \(\frac{T}{3}\) |
3. | \(\frac{T}{12}\) | 4. | \(\frac{T}{6}\) |
Force on a particle F varies with time t as shown in the given graph. The displacement x vs time t graph corresponding to the force-time graph will be:
1. | 2. | ||
3. | 4. |
The time period of a simple pendulum in a stationary trolley is \(T_1.\) If the trolley is moving with a constant speed, then time period is \(T_2,\) then:
1. \(T_1>T _2\)
2. \(T_1<T _2\)
3. \(T_1=T _2\)
4. \(T_2= \infty \)
A particle executes SHM with a frequency of \(20\) Hz. The frequency with which its potential energy oscillates is:
1. \(5\) Hz
2. \(20\) Hz
3. \(10\) Hz
4. \(40\) Hz
A particle is moving along the x-axis. The speed of particle v varies with position x as . The time period of S.H.M is
1.
2.
3.
4.