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A solid cylindrical steel column is 4 mlong and 9 cm in diameter .$ ( Y_{steel} = 1.9 \times 10^{11} Nm^{-2} ) $ The decrease in length of the column, while carrying a load of 80000 kg is...........
$ y = { FL \over Al } $
A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. Amassless piston of area Afloats on the surface of the liquid. When a massM is placed on the pisten to compress the liquid, the fractional change in the radius of the sphere $ \delta R \over R $ is
$ K = { p \over \left ( { dV \over V} \right ) } = { Mg \over A \left ( dV \over V \right) } \Rightarrow { dV \over V } = { Mg \over KA } $ Now , $ V = { 4 \over 3 } \pi R^3 $ $ ln V= ln (4/3 \pi ) + 3 ln R $ Differentiation $ {dV \over V} = { 3dR \over R } = { Mg \over KA } \Rightarrow { dR \over R } = { mg \over 3KA } $
In a Searle's experiment, the diameter of the wire as measured bya screw gauge of least count 0.1 m, is 110.0 cm. When a weight of 50N is suspended from the wire, the extension is measured to 0.125 cm bya micrometer ofleast count 0.001 cmthe maximumerror in themeasurement of Young's modulus of the material of the wire is N/m2 ?
Young's modulus of elasticity is given by $ Y = { stress \over strain } = { F/A \over l / A} = { FL \over LA } = { FL \over l ( {\pi d^2 \over 4 }) } $ Substituting the values , we get $ Y = 2.24 \times 10^{11} N/m^2 $ Now $ { \triangle y \over y } = { \triangle L \over L } + { \triangle l \over l } + 2 { \triangle d \over d } $ Substituting the values , ${ \triangle y \over y } = 0.0489 $
The amount of energy evolved when eight droplets of mercury(surface tension 0.55 Nm-1) of radius 1 mm each combine into one drop is ........
Using the formula $ W = T \triangle A $
To what height can mercury be filled in a ressel without any leakage if there is a pinhole of diameter 0.1 m mat the bottom of the vessel. ($ Density of mercury = 13.6 \times 10^3 kg m^ {-3} $ , surface tension of mercury = $ 550 \times 10 h^{-3} \rho Nm^{-1} , Angle of contact with the vessel for mercury = 0 ^\circ $ )
Mercury will start leaking when $ \rho g h = { 2T \over r } $ $ h_{min} = { 2T \over \rho gr} = { 4T \over \rho g d } $
A spherical soap bubble of radius 2 cm attached to the outside of a spherical bubble of radius 4 cm. Then what is the radius of the common surface ?
$P_2 - P_1 = 4T \left( {1 \over r_2 } - { 1 \over r_1} \right) = { 4T \over r } $ $ { 1 \over r } = { 1 \over r_2} - { 1 \over r_1} = { 1 \over 2 } - { 1 \over 4 } = { 1 \over 4 } \Rightarrow r = 4 cm $
By how much depth will the surface of a liquid be depressed in a glass tube of radius 0.2 mm if the angle of contact of the liquid is $135 ^\circ $ and the surface tension is $0.547 Nm^{-1}$ ? (Density of the liquid is $kg m^{-3}$)
$ h = { 2 T cos \theta \over \rho . g . r } $
Complete the sentence If the height of a capillary is smaller than the height to which water should rise, then........
$ T = { h \rho g r \over 2 cos \theta } $ If h is not sufficient, then $ \theta $ changes h takes on the value of the length of the tube.
The velocity of a small ball of mass m and density $d_1$ when dropped in a container filled with glycerine becomes constants after sometime. What is the viscous force acting on the ball ? (density of glycerine is $d_2$)
$ viscous force = weigth - bouyant force $ $ = V d_1 g - Vd_2 g = Vd_1g \left[ 1 -{ d_2 \over d_1 } \right] = mg \left( 1 - {d_2 \over d_1} \right) $
A boat of area $10 m^2$ floating on the surface of a river is made to move horizontaly with a speed of $2 ms^{-1} $ by applying a tangential force. If the river is 1m deep and the water in contact withthe bed is stationary, what is the tangential force needed to keep the boat moving ? (viscosity of water 0.01 poise)
$ velocity gradient = { dv \over dx} $ $ F = - \eta A { dv \over dx } $ Tangential force is equal and opposite to the viscous force
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