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A cube of mass m and density D is suspen...

A cube of mass `m` and density `D` is suspended from a point `P` by a spring of stiffness `k`. The system is kept inside a beaker filled with a liquid of density `d`. The elongation in the spring, assuming `D gt d`, is :

A

`(mg)/k (1-d/D)`

B

`(mg)/1 (1-D/d)`

C

`(mg)/k (1+d/D)`

D

None of these

Text Solution

Verified by Experts

The cube is in equilibrium under the following three forces ,
spring force kx , where x = elongation of the spring ,
gravitional force w , weight of the cube = mg
buoyant force `F_(b)` ( or upward thrust ) imparted by the liquid on the cube given as `F_(b) = Vdg` where V = volume of the immersed portion of the cube equilibrium of the cube , ` kx + F_(b) = mg`
`rArr x = (mg -F_(b))/(k) = (mg- Vdg)/k ` where V = volume he immersed portion of the cube , For complete immersion , V = volume of the cube
For equilibrium of the cube , ` kx + F_(b) = mg`
` rArr = (mg-F_(b))/k = (mg-Vdg)/k ` Where V = (m/D)
` rArr x = (mg)/k (1- d/D)`
Hence (A) is correct
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Knowledge Check

  • A sphere of density d is let fall in a liquid of density (d)/(4) . The acceleration of the body will be

    A
    `(g)/(4)`
    B
    `(3g)/(4)`
    C
    `(g)/(2)`
    D
    g

  • A disc of mass m is connected with an ideal spring of stiffness k . If it is released from rest, it rolls without sliding on an inclination plane. The maximum elongation of the spring is:

    A
    `(mg sin theta)/k`
    B
    `(2mg sin theta)/(3k)`
    C
    `(3mg sin theta)/k`
    D
    `(2 mg sin theta)/k`

  • A body of volume V and density d is completely immersed in a liquid of density p. Then the apparent weight of the body will be:

    A
    Vdg
    B
    `V rho g`
    C
    `V(rho -d)g`
    D
    `V(d-rho)g`