Home
Class 11
PHYSICS
A wooden plank of length 1m and uniform ...

A wooden plank of length 1m and uniform cross-section is hinged at one end to the bottom of a tank as shown in fig. The tank is filled with water upto a hight 0.5m. The specific gravity of the plank is 0.5. Find the angle `theta` that the plank makes with the vertical in the equilibrium position. (Exclude the case `theta=theta^@`)

Text Solution

Verified by Experts

The correct Answer is:
D

`OA=(OB)/(2)=(0.5 sec theta)/(2)=0.25 sec(theta)`
About point `O`, clockwise moment of
`w=` anticlockwise moment of `F`.
`:. w(L/2 sin theta)=F(OA sin theta)=F(0.25 sin theta. sec theta)`
Given, `L=1m`
`:. cos theta =(F)/(2w)=((0.5 sec theta)(A)(1.0)g)/(2(1)(A)(0.5)g)`
or, `cos^(2)theta=1/2, cos theta=(1)/(sqrt(2))`
`:. theta=45^(@)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • FLUID MECHANICS

    DC PANDEY|Exercise Example 13.1|1 Videos

  • FLUID MECHANICS

    DC PANDEY|Exercise Example 13.2|1 Videos

  • FLUID MECHANICS

    DC PANDEY|Exercise Level 2 Comprehension Based|7 Videos

  • EXPERIMENTS

    DC PANDEY|Exercise Subjective|15 Videos

  • GENERAL PHYSICS

    DC PANDEY|Exercise INTEGER_TYPE|2 Videos

Similar Questions

Explore conceptually related problems

The wooden plank of length 1 m and uniform cross section is hinged at one end to the bottom of a tank as shown in figure. The tank is filled with water up to a height of 0.5 m. The specific gravity of the plank is 0.5. Find the angle theta that the plank makes with the vertical in the equilibrium position. (Exclude the case theta=0 ) ,

A wooden plank of length 1m and uniform cross-section is hinged at one end of the bottom of tank as shown in figure. The tank is filled with water upto a height of 0.5 m . Find the angle theta that the plank makes with the vertical in the equilibrium position. [Exclude the case thea = 0 ]

Knowledge Check

  • A wooden rod of a uniform cross section and of length 120 cm is hinged at the bottom of the tank which is filled with water to a height of 40 cm . In the equilibrium position, the rod makes an angle of 60^@ with the vertical. The centre of buoyancy is located on the rod at a distance (from the hinge) of

    A
    `20cm`
    B
    `40cm`
    C
    `60cm`
    D
    `75cm`

  • A uniform rod of length 2.0 m specific gravity 0.5 and mass 2 kg is hinged at one end to the bottom of a tank of water (specific gravity = 10) filled upto a height o f 1.0 m as shown in figure. Taking the case theta =- 0^(@) the force exerted by the hings on the rod is (g = 10 m//s^(2))

    A
    10.2 N upwards
    B
    4.2 N downwards
    C
    8.3 N downwards
    D
    6.2 N upwards

    • Similar Questions

    Explore conceptually related problems

    Two non-viscous, incomoressible and immiscible liquids of densities rho and 1.5 rho are poured into the two limbs of a circules tube of radius R and small cross-section kept fixed in a vertical plane as shown in fig. Each liquid occupies one-fourth the cirumference of the tube. (a) Find the angle theta the radius to the interface makes with the vertical in equilibrium position. (b) If the whole liquid column is given a small displacement from its equilibrium position, show that the resulting oscillations alre simple harmonic. Find the time period of these oscillations.

    Two non-viscous, incompressible and immiscible liquids of densities p and 1.5p are poured into the two limbs of a circular tube of radius R and small cross section kept fixed in a vertical plane as shown in the figure. Each liquid occupies one fourth the circumference of the tube. (i)Find the angle theta that the radius to the interface makes with the vertical in equilibrium position. _________ (ii) If the whole liquid column is given a small displacement from its equilibrium position, show that the resulting oscillations are simple harmonic. Find the time period of these oscillations. ____________

    A tank of square cross section (2mxx2m) is filled with water up to a height of 2.5 m . Find the thrust experienced by the vertical and botom of the tank (g=10m//s^(2)) .

    A uniform wooden bar of length l and mass m hinged on a vertical wall of a containing water, at one end. 3//5th part of the bar is submerged in water. Find the ratio of densities of the liquid and the bar.

    A box of mass 4 kg is placed on a wooden plank of length 1.5 m which is lying on the ground. The plank is lifted from one end along its length so that it becomes inclined. It is noted that when the vertical height of the top end of the plank from the ground becomes 0.5 m, the box begins to slide. Find the coefficient of friction between the box and the plank.

    A conical pendulum, a thin uniform rod of length l and mass m , rotates uniformly about a vertical axis with angular velocity omega (the upper end of the rod is hinged). Find the angle theta between the rod and the vertical.

    Home
    Profile