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. \(l_A = \frac{l_B}{4}\)
2. \(l_A= 4l_B\)
3. \(l_A= 2l_B~\&~M_A=2M_B\)
4. \(l_A= \frac{l_B}{2}~\&~M_A=\frac{M_B}{2}\)
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 |
1. | \(2n\) | 2. | \(n/2\) |
3. | \(n\) | 4. | none of the above |
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.
When an oscillator completes 100 oscillations, its amplitude is reduced to of the initial value. What will be its amplitude, when it completes 200 oscillations?
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. \(\frac{T}{4}\)
2. \(T\)
3. \(\frac{T}{2}\)
4. \(2T\)