Home
Class 11
PHYSICS
A cylindrical plastic bottle of negligib...

A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic montion angular frequency `omega`. If the radius of the bottle is 2.5 cm then `omega` is close to: (density of water `= 10^(3) kg//m^(3)`)

A

`2.50 rad s^(-1)`

B

`3.75 rad s^(-1)`

C

`8.00 rad s^(-1)`

D

`1.25 rad s^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`mg = B_(C) = rho Ahg `
ma = B - mg
` - ma = rho A ( h + Delta h) g - rho Ahg`
`- ma = rho Ag (Delta h)`
`a = ( - rho Ag Delta h)/( m)`
`omega = sqrt(( 10^(3) xx A xx g)/( 310 xx 10 ^(-3)))`
`= sqrt(( 10^(3) xx pi xx 6.25 xx 10 ^(-4) xx 10)/( 310 xx 10 ^(-3) xx 100)) = sqrt( 62.5) ~~ 8 ` rad /s
Promotional Banner

Similar Questions

Explore conceptually related problems

A 0.1kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its crosssectional are is 4.9xx10^-7m^2 . If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s^-1 . If the Young's modulus of the material of the wire is nxx10^9 Nm^-2 , the value of n is

A mass of 0.2 kg, length 1m and cross sectional area 4.9 xx 10^(-7) m^(2) is suspended from a massless wire. The mass is pulled slightly in the vertically downward direction and released. It performs simple harmonic motion of angular frequency 70 rad s^(-1) . If the Young's modulus of the material of the wire is x xx 10^(9) Nm^(-2) , find the value of x.

A wooden cube floating in water supports a mass 0.2 kg on its top. When the mass is removed the cube rises by 2cm. What is the side legnth of the cube ? Density of water = 10^3 kg//m^3

Water form a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flo0w is : (density of water =1000kg//m^(3) , coefficient of viscosity of water =1mPas)

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10^(-3) Pa s, respectively. (Density of water : 10^(3) kg//m^(2))

A boat having a length 4m and breadth 2.5 m is floating on lake. The boat sinks by 2 cm when a load is loaded on it. What is the weight of the load ? Use g =10 ms^(-2), density of water = 10^3 kg m^(-3)

A bottle has a thin nozzle on top. It is filled with water, held horizontally at a height of 1 m and squeezed slowly by hands so that the water jet coming out of the nozzle hits the ground at a distance of 2m . If the area over which the hands squeeze it is 10 cm^2. the force applied by hand is close to (take g= 10 m//s^2 and density of water= 1000 kg//m^3 )

Two blocks A and B having mass m = 1 kg and M = 4 kg respectively are attached to a spring and placed vertically on a weighing machine as shown in the figure. Block A is held so that the spring is relaxed. A is released from this position and it performs simple harmonic motion with angular frequency w = 25 rad s^(-1) . The spring remains vertical (a) Find the reading of the weighing machine as a function of time. Take t = 0 when A is released. (b) What is the maximum reading of the weighing machine ?

The terminal velocity of a water drop of radius 0.01 mm falling through air is 1.12 cm/s. If the density of air is neglected, the coefficient of viscosity of air is [density of water =10^(3) kg//m^(3), g=9.8m//s^(2)]