Question

 

A rod of length 6 m has a mass 12 kg. It is hinged at one end at a distance of 3 m below water surface. (a) What weight must be attached to the other end of the rod so that 5 m of the rod are submerged? (b) Find the magnitude and direction of the force exerted by the hinge on the rod. 

(Specific gravity of rod is 0.5).

Solution

Correct option is

8 g, 5.67 kg

 

As shown in figure, the forces acting on the rod are : 

(1) The weight of rod 12 g N acting downwards through the CG of the rod, i.e., at a distance of 3 m from the hinge. 

(2) Force of buoyancy through the CG of displacement liquid vertically upwards. As

 

                    

Force of buoyancy 

                 

and acts at a distance 2.5 m from the hinge  

(3) Extra weight w at the other end of the rod at a distance 6 m from Oacting vertically downwards.  

(4) Reaction R at the hinge at O will be vertical (as here all the forces are vertical, so for horizontal equilibrium of the rod RH = 0)

So for translator equilibrium of rod, 

         

And for rotational equilibrium of rod (taking moments about O

        

Substituting the value of w from eq. (ii) in (i) and solving for R, we get 

            

Negative sign implies that R is directed vertically downwards.   

SIMILAR QUESTIONS

Q1

A block of wood floats in water with two-thirds of its volume submerged. In oil the block floats with 0.90 of its volume submerged. Find the density of (a) wood and (b) oil, if density of water is 103 kg/m3  

Q2

Air is streaming past a horizontal aeroplane wing such that its speed is 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg/m3, find the difference in pressure between the top and bottom of the wing. If the wing is 10 m long and has an average width 2m, calculate the gross lift of the wing. 

Q3

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where the cross-section area is 10 cm2, the water velocity is 1 m/s and the pressure is 2000 Pa. What is the pressure of water at another point where the cross-section area is 5 cm2?

Q4

Water from a tap emerges vertically downward with an initial speed of 1.0 ms–1. The cross-sectional area of the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is : (g = 10 m/s2 

Q5

Water is filled in a cylindrical container upto a height of 3 m. A hole of cross-section area a is made in the wall of the container at a height of 52.5 cm from the bottom. The cross-section area of the container is A. If a/A = 0.1, then the squire of the speed of water coming out from the hole is (g = 10 m/s2)

Q6

The vertical section of a wing of a fan is shown below. Maximum upthrust is in

                                            

Q7

The vertical of a mass ball of mass M and density d1, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d2, the viscous force acting on the ball will be

Q8

To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid passes on the side of the vessel equal to the force exerted be the liquid on the bottom of the vessel?

Q9

 

The density of air in atmosphere decreases with height and can be expressed by the relation:  

           

Where  is the density at sea-level, A is a constant and h is the height. Calculate the atmospheric pressure at sea-level. Assume g to be constant. 

Q10

 

A large block of ice 5 m thick has a vertical hole drilled through it floating in the middle of a lake. What is the minimum length of a rope required to scoop up a bucket full of water through the hole?

[RD of ice = 0.9]