Home
Class 12
PHYSICS
A solid cylinder of denisty rho(0), cros...

A solid cylinder of denisty `rho_(0)`, cross-section area A and length `l` floats in a liquid `rho(gtrho_(0)` with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be :

A

`2pisqrt((l)/(g))`

B

`2pisqrt((rho_(0)l)/(rhog))`

C

`2pisqrt((rhol)/(rho_(0)g))`

D

`2pisqrt((l)/(2g))`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • RACE

    ALLEN |Exercise Basic Maths (Wave Motion & Dopplers Effect) (Fundamental)|24 Videos
  • RACE

    ALLEN |Exercise Basic Maths (Wave Motion & Dopplers Effect) (Superposition of waves interfarence, beats)|15 Videos
  • RACE

    ALLEN |Exercise Basic Maths (Oscillations) (Energy & spring pendulum)|17 Videos
  • NEWTONS LAWS OF MOTION

    ALLEN |Exercise EXERCISE-III|28 Videos
  • SIMPLE HARMONIC MOTION

    ALLEN |Exercise Example|1 Videos

Similar Questions

Explore conceptually related problems

A homogeneous solid cylinder of length L(LltH/2), cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure P_0 . Then density D of solid is given by

A wooden cube (density of wood 'd' ) of side 'l' flotes in a liquid of density 'rho' with its upper and lower surfaces horizonta. If the cube is pushed slightly down and released, it performs simple harmonic motion of period 'T' . Then, 'T' is equal to :-

A container of large uniform cross-sectional area A resting on a horizontal surface, holes two immiscible, non-viscon and incompressible liquids of densities d and 2d each of height H//2 as shown in the figure. The lower density liquid is open to the atmosphere having pressure P_(0) . A homogeneous solid cylinder of length L(LltH//2) and cross-sectional area A//5 is immeresed such that it floats with its axis vertical at the liquid-liquid interface with length L//4 in the denser liquid, The cylinder is then removed and the original arrangement is restroed. a tiny hole of area s(sltltA) is punched on the vertical side of the container at a height h(hltH//2) . As a result of this, liquid starts flowing out of the hole with a range x on the horizontal surface. The total pressure with cylinder, at the bottom of the container is

A cylindrical of wood (density = 600 kg m^(-3) ) of base area 30 cm^(2) and height 54 cm , floats in a liquid of density 900 kg^(-3) The block is displaced slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :

A cylindrical piece of cork of density of base area A and height h floats in a liquid of density p_(l) . The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T=2pisqrt((hp)/(p_(1)g)) where p is the density of cork. (Ignore damping due to viscosity of the liquid).

One end of a long metallic wire of length (L) is tied to the ceiling. The other end is tied to a massless spring of spring constant . (K.A) mass (m) hangs freely from the free end of the spring. The area of cross- section and the Young's modulus of the wire are (A) and (Y) respectively. If the mass is slightly pulled down and released, it will oscillate with a time period (T) equal to :

A metal wire of uniform cross-sectional area A and length L, has mass m. It is suspended vertically from a ceiling. If its Young's modulus is Y, then the elongation Deltal of wire due to its own weight will be .........

An ideal gas enclosed in a cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium, the volume of the gas is V_(0) and its pressure is P_(0) . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

A cylinderical rod of length l=2m & density (rho)/(2) floats vertically in a liquid of density rho as shown in figure (i). Show that it performs SHM when pulled slightly up & released find its time period. Neglect change in liquid level. (ii). Find the time taken by the rod to completely immerse when released from position shown in (b). Assume that it remains vertical throughout its motion (take g=pi^(2)m//s^(2) )

A solid sphere of density rho= rho_(0) (1 - (r^(2))/(R^(2))), 0 lt r le R just floats in a liquid, then the density of the liquid is (r is the distance from the centre of the sphere)

ALLEN -RACE-Basic Maths (Oscillations) (Simple pendulum and types of SHM)
  1. Two pendulums of length 1.21 m and 1.0 m starts vibrationg. At some in...

    Text Solution

    |

  2. The length of a simple pendulum is increased by 44%. The percentage in...

    Text Solution

    |

  3. A solid cylinder of denisty rho(0), cross-section area A and length l ...

    Text Solution

    |

  4. A 100 g mass stretches a particular spring by 9.8 cm, when suspended v...

    Text Solution

    |

  5. When a block of mass m is suspended separately by two different spring...

    Text Solution

    |

  6. In forced oscillations , a particle oscillates simple harmonically wit...

    Text Solution

    |

  7. A simple pendulum of length 40 cm oscillates with an angular amplitude...

    Text Solution

    |

  8. The time period and the amplitude of a simple pendulum are 4 seconds a...

    Text Solution

    |

  9. A simple pendulum of length 1m is attached to the ceiling of an elevat...

    Text Solution

    |

  10. A pendulum has a period T for small osillations. An obstacle is placed...

    Text Solution

    |

  11. The position vector of a aprticle is given as vecr=(5t^2-4t+6)hati+(t^...

    Text Solution

    |

  12. Choose the correct statement :-

    Text Solution

    |

  13. A simple pendulum has a time period T in vacuum. Its time period when ...

    Text Solution

    |

  14. The time period of a simple pendulum in a stationary train is T. The t...

    Text Solution

    |

  15. The amplitude of damped oscillator becomes 1/3 of original value in 2s...

    Text Solution

    |

  16. Amplitude of a damped oscillator decreases up to 0.6 times of its init...

    Text Solution

    |

  17. A simple pendulm has a length L and a bob of mass M. The bob is vibrat...

    Text Solution

    |