A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the
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  • 1
    Two capillaries of same length and radii in the ratio $1 : 2$  are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is $ 1 m$  of water, the pressure difference across first capillary is...... $m$
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  • 2
    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 $3 p$. The complete arrangement is placed in a liquid of density $2 p$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are)

    $(A)$ the net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$

    $(B)$ the net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$

    $(C)$ the light sphere is partially submerged.

    $(D)$ the light sphere is completely submerged.

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  • 3
    Figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on vertical line and points $B$ and $D$ lie on horizontal line. The incorrect statement is $\left(p_A, p_B, p_C, p_D\right.$ are absolute pressure at the respective points)
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  • 4
    A block of steel of size $ 5 cm × 5 cm × 5 cm $ is weighed in water. If the relative density of steel is $7,$  its apparent weight is
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  • 5
    If velocity of flow is $4 \,m / s$, then velocity head is .........$m$
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  • 6
    Density of ice is $\rho $ and that of water is $\sigma $. What will be the decrease in volume when a mass $M$  of ice melts
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  • 7
    A cylindrical vessel filled with water is released on an inclined surface of angle $\theta$ as shown in figure.The friction coefficient of surface with vessel is $\mu( < \tan \theta)$.Then the contact angle made by the surface of water with the incline will be
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  • 8
    The velocity of water in a river is $18\, km/h$ near the surface. If the river is $5\, m$ deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water $= 10^{-2}\,,poise$
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  • 9
    A drinking straw is dipped in a pan of water to depth d from the surface (see figure below). Now water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result, its height $y$ from the surface of the water varies periodically. Ignoring damping, the equation for $y$ is ( $g$ is the acceleration due to gravity):
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  • 10
    The two thigh bones (femures), each of cross-sectional area $10 \,cm ^2$ support the upper part of a person of mass $50 \,kg$. The average pressure sustained by the femures is ............. $N / m ^2$
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