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During a painting process, a thin, flat ...

During a painting process, a thin, flat tape of width b (dimension perpendicular to the plane of the figure) is pulled through a paint filled channel of length L. The density and viscosity of the paint liquid is `rho` and `eta` respectively. The tape is pulled at a constant speed v and width of the channel is h. Find the minimum force needed to pull the tape.

Answer

Step by step text solution for During a painting process, a thin, flat tape of width b (dimension perpendicular to the plane of the figure) is pulled through a paint filled channel of length L. The density and viscosity of the paint liquid is rho and eta respectively. The tape is pulled at a constant speed v and width of the channel is h. Find the minimum force needed to pull the tape. by PHYSICS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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(i) A non uniform cube of side length a is kept inside a container as shown in the figure. The average density of the material of the cube is 2 rho where rho is the density of water. Water is gradually fille din the container. It is observed that the cube begins to topple, about its edge into the plane of the figure passing through pointA, when the height of the water in the container becomes (a)/(2) . Find the distance of the centre of mass of the cube from the face AB of the cube. Assume that water seeps under the cube. (ii) A rectangular concrete block (specific gravity =2.5) is used as a retatining wall in a reservoir of water. The height and width of the block are x and y respectively the height of water in the reservoir is z=(3)/(4)x . the concrete block cannot slide on the horizontal base but can rotate about an axis perpendicular to the plane of the figure and passing through point A (a) Calculate the minimum value of the ratio (y)/(x) for which the block will not begin to overturn about A. (b) Redo the above problem for the case when there is a seepage and a thin film of water is present under the block. Assume that a seal at A prevents the water from flowing out underneath the block.

A heavy rope of mass m and length 2L is hanged on a smooth little peg with equal lengths on two sides of the peg. Right part of the rope is pulled a little longer and released. The rope begins to slide under the action of gravity. There is a smooth cover on the peg (so that the rope passes through the narrow channel formed between the peg and the cover) to prevent the rope from whiplashing. (a) Calculate the speed of the rope as a function of its length (x) on the right side. (b) Differentiate the expression obtained in (a) to find the acceleration of the rope as a function of x. (c) Write the rate of change of momentum of the rope as a function of x. Take downward direction as positive (d) Find the force applied by the rope on the peg as a function of x. (e) For what value of x, the force found in (d) becomes zero? What will happen if there is no cover around the peg ?

Knowledge Check

  • In a thin rectangular metallic strip a constant current I flows along the positive x-direction , as shown in the figure. The length , width and thickness of the strip are l, w and d , respectively. A uniform magnetic field vec(B) is applied on the strip along the positive y- direction . Due to this, the charge carriers experience a net deflection along the z- direction . This results in accumulation of charge carriers on the surface PQRS ansd apperance of equal and opposite charges on the face opposite to PQRS . A potential difference along the z-direction is thus developed. Charge accumulation contiues untill the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross- section of the strip and carried by electrons. Consider two different metallic strips (1 and 2) of the same material . Their lengths are the same,widths are w_(1) and w_(2) and thickness are d_(1) and d_(2) respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane ( see figure) . V_(1) and V_(2) are the potential differences between K and M in strips 1 and 2 , respectively . Then, for a given current I flowing through them in a given magnetic field strength B , the correct statement(s) is (are)

    A
    If ` w_(1) = w_(2) and d_(1) = 2d_(2), then V_(2) = 2V_(1)`
    B
    If ` w_(1) = w_(2) and d_(1) = 2d_(2), then V_(2) = V_(1)`
    C
    If ` w_(1) = 2w_(2) and d_(1) = d_(2), then V_(2) = 2V_(1)`
    D
    If ` w_(1) = 2w_(2) and d_(1) = 2d_(2), then V_(2) = V_(1)`

  • In a thin rectangular metallic strip a constant current I flows along the positive x-direction , as shown in the figure. The length , width and thickness of the strip are l, w and d , respectively. A uniform magnetic field vec(B) is applied on the strip along the positive y- direction . Due to this, the charge carriers experience a net deflection along the z- direction . This results in accumulation of charge carriers on the surface PQRS ansd apperance of equal and opposite charges on the face opposite to PQRS . A potential difference along the z-direction is thus developed. Charge accumulation contiues untill the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross- section of the strip and carried by electrons. Consider two different metallic strips (1 and 2) of same dimensions n_(1) and n_(2) , repectrively . Strip 1 is placed in magnetic field B_(1) and strip 2 is placed in magnetic field B_(2) , both along positive y- directions . Then V_(1) and V_(2) are the potential differences developed between K and M in strips 1 and 2 , respectively . Assuming that the current I is the same for both the strips, the correct option(s) is (are)

    A
    If `B_(1) = B_(2) and n_(1) = 2n_(2), then V_(2) = 2V_(1)`
    B
    If `B_(1) = B_(2) and n_(1) = 2n_(2), then V_(2) = V_(1)`
    C
    If `B_(1) = 2B_(2) and n_(1) = 2n_(2), then V_(2) = 0.5 V_(1)`
    D
    If `B_(1) = 2B_(2) and n_(1) = 2n_(2), then V_(2) = V_(1)`

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