A spring of force constant k is cut into two equal halves. The force constant of each half is
For a force F, the extension x in a spring of force constant k is given by
F = kx
Now extension is proportional to the length of the spring. When the spring is cut into two equal halves, the extension x’ of each half, for a force F will be x’ = x/2. If k’ is the force constant of each half, we have
Comparing (i) and (ii) we get
A simple pendulum with a brass bob has a time period T. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is 1/8 that of brass, the time period of the same pendulum will be
A simple pendulum of frequency f has a metal bob. If the bob is charged negatively and is allowed to oscillate with a positively charged plate placed under it, the frequency will
A wooden block is suspended from a spring. Its period for vertical oscillations is T. In a second experiment the same apparatus is laid on a horizontal frictionless table with the free end of the spring fixed to a nail on the table. The block is pulled a little so as to stretch the spring and then released. The mass will
The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 parts of hydrogen and 2 parts of oxygen at STP will be.
A solid brass sphere is hung from a spring whose mass is negligible compared to that of the sphere. The sphere is set into vertical oscillations and its time period is found to be T. The sphere is now completely immersed in a liquid whose density is 1/8th that of brass. The time period of vertical oscillations with the sphere always remaining immersed in the liquid will be equal to
A heavy metal sphere is suspended from a spring. When pulled down a little and released, it oscillates up and down with a frequency f. If it is taken to the moon (where the acceleration due to gravity is one-sixth that on earth) the frequency of vertical oscillation will
A mass M attached to a light spring oscillates with a period of 2 seconds. If the mass is increased by 2 kg the period increases by 1 second. What is the value of M?
A simple harmonic motion is given by the equation
Where x is in metres. The amplitude of the motion is
Figure shows three identical springs A, B, C. When a 4 kg weight is hung on A, it descends by 1 cm. When a 6 kg weight is hung on C, it will descent by
Two springs of equal lengths and equal cross-sectional areas are made of materials whose Young’s modulii are in the ratio of 3:2. They suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of