Two spherical bobs of masses \(M_A\) and \(M_B\) are hung vertically from two strings of length \(l_A\) and \(l_B\) respectively. If they are executing SHM with frequency as per the relation \(f_A=2f_B,\) Then:
1.
2.
3.
4.
The circular motion of a particle with constant speed is:
1. | Periodic and simple harmonic | 2. | Simple harmonic but not periodic |
3. | Neither periodic nor simple harmonic | 4. | Periodic but not simple harmonic |
The frequency of a spring is \(n\) after suspending mass \(M.\) Now, after mass \(4M\) mass is suspended from the spring, the frequency will be:
1. | \(2n\) | 2. | \(n/2\) |
3. | \(n\) | 4. | none of the above |
Which one of the following statements is true for the speed 'v' and the acceleration 'a' of a particle executing simple harmonic motion?
1. | The value of a is zero whatever may be the value of 'v'. |
2. | When 'v' is zero, a is zero. |
3. | When 'v' is maximum, a is zero. |
4. | When 'v' is maximum, a is maximum. |
A spring elongates by a length 'L' when a mass 'M' is suspended to it. Now a tiny mass 'm' is attached to the mass 'M' and then released. The new time period of oscillation will be:
1. \(2 \pi \sqrt{\frac{\left(\right. M + m \left.\right) l}{Mg}}\)
2. \(2 \pi \sqrt{\frac{ml}{Mg}}\)
3. \(2 \pi \sqrt{L / g}\)
4. \(2 \pi \sqrt{\frac{Ml}{\left(\right. m + M \left.\right) g}}\)
The frequency of a simple pendulum in a free-falling lift will be:
1. zero
2. infinite
3. can't say
4. finite
When a mass is suspended separately by two different springs, in successive order, then the time period of oscillations is \(t _1\) and \(t_2\) respectively. If it is connected by both springs as shown in the figure below, then the time period of oscillation becomes \(t_0.\) The correct relation between \(t_0,\) \(t_1\) & \(t_2\) is:
1.
2.
3.
4.
The displacement between the maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is:
1.
2.
3.
4.
The time period of a mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:
1. T/4
2. T
3. T/2
4. 2T
A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:
1. | 2. | ||
3. | 4. |