Home
Class 11
PHYSICS
A wooden stick of length L, radius R and...

A wooden stick of length `L`, radius `R` and density `rho` has a small metal piece of mass `m` ( of negligible volume) attached to its one end. Find the minimum value for the mass `m` (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density `sigma(gtrho)`.

Text Solution

Verified by Experts

The correct Answer is:
`piR^(2)L(sqrt(rhosigma)-rho)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN |Exercise Exercise 5 B (Integer Type Questions)|3 Videos

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN |Exercise Exercise 5 B (Assertion Reason)|1 Videos

  • CENTRE OF MASS

    ALLEN |Exercise EXERCISE-V B|19 Videos

  • ERROR AND MEASUREMENT

    ALLEN |Exercise Part-2(Exercise-2)(B)|22 Videos

Similar Questions

Explore conceptually related problems

A solid sphere of radius R and density rho is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3rho . The complete arrangement is placed in a liquid of density 2rho and is allowed to reach equilibrium. The correct statements(s) is (are)

A simple pendulum of bob of mass m and length L has one of its ends fixed at the centre O of a vertical circle, as shown in the figure. If 0=60^(@) at the point P , the minimum speed u that should be given to the bob so that it completes vetical circle is

A cylinderical container of length L is full to the brim with a liquid which has mass density rho . It is placed on a weight scale, the scale reading is w. A light wall ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left Q. if instead of being pushed down by a rod, the ball is held in place by a thin string attached to the bottom of the container as shown on the right what is the tension T is the string? (a). (rhoV-m)g (b). rhoVg (c). mg (d). none of these

An almost inertia-less rod of length l3.5 m can rotate freely around a horizontal axis passing through its top end. At the bottom end of the roa a small ball of mass m andat the mid-point another small ball of mass 3m is attached. Find the angular frequency (in SI units) of small oscillations of the system about the equilibrium position. Gravitational acceleration is g=9.8 m//s^(2).

A cylinderical container of length L is full to the brim with a liquid which has mass density rho . It is placed on a weight scale, the scale reading is w. A light wall ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left Q. What is the mass M of liquid which overflowed while the ball was being pushed into the liquid? (a). rhoV (b). m (c). m-rhoV (d). none of these

A small uniform tube is bent into a circle of radius r whose plane is vertical. Equal volumes of two fluids whose densities are rho and sigma(rhogtsigma) fill half the circle. Find the angle that the radius passing through the interface makes with the vertical.

A small ring of mass m_(1) is connected by a string of length l to a small heavy bob of mass m_(2) . The ring os free to move (slide) along a fixed smooth horizontal wire. The bob is given a small displacement from its equilibrium position at right angles to string. Find period of small oscillations.

A non-conducting disc of radius a and uniform positive surface charge density sigma is placed on the ground, with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disc, from a height H with zero initial velocity. The particle has q//m=4 in_0 g//sigma (a) Find the value of H if the particle just reaches the disc. (b) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.

A non-uniform rod of mass m , length l and radius r is having its centre of mass at a distance l//4 from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density rho . The moment of inertia of the rod about the centre of mass is I . The angular acceleration of point A relative to point B just after the rod is released from the position as shown in the figure is

A thin homogeneous rod of mass m and length l is free to rotate in vertical plane about a horizontal axle pivoted at one end of the rod. A small ballof mass m and charge q is attached to the opposite end of this rod. The whole system is positioned in a horizontal electric field of magnitude E=(mg)/(2q) . The rod is released from, shown position from rest. What is the acceleration of the small ball at the instant of releasing the rod?

Home
Profile