14: Some Mechanical Properties Of Matter : Neet-xii-physics

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NEET-XII-Physics

14: Some Mechanical Properties of Matter

with Solutions - page 3

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Qstn #9
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
(a) when the mass is at the highest point
(b) when the mass is at the lowest point
(c) when the wire is horizontal
(d) at an angle of cos^-1(1/3) from the upward vertical.
digAnsr: b
Ans : (b)
If the velocity of the mass is a maximum at the bottom, then the string experiences tension due to both the weight of the mass and the high centrifugal force. Both these factors weigh the mass downwards. The tension is therefore, maximum at the lowest point, causing the string to most likely break at the bottom.
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Qstn #10
When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.
(a) This energy completely appears as the increased kinetic energy of the block.
(b) This energy completely appears as the increased elastic potential energy of the wire
(c) This energy completely appears as heat.
(d) None of these.
digAnsr: d
Ans : (d)
None of these is the correct option. The decreased gravitational potential energy transforms partly as elastic energy, partly as kinetic energy and also in the form of dissipated heat energy.
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Qstn #11
By a surface of a liquid we mean
(a) a geometrical plane like x = 0
(b) all molecules exposed to the atmosphere
(c) a layer of thickness of the order of 10^-8m
(d) a layer of thickness of the order of 10^-4m
digAnsr: c
Ans : The correct option is
(c).
The surface of a liquid refers to the layer of molecules that have higher potential energy than the bulk of the liquid. This layer is typically 10 to 15 times the diameter of the molecule. Now, the size of an average molecule is around 1 nm = `` {10}^{-9}``m, so a diameter of 10 to 15 times would be of order `` 10\times {10}^{-9}={10}^{-8}`` m.
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Qstn #12
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
(a) will retain its cubical shape
(b) will change its shape to spherical
(c) will fall down on the floor of the hall
(d) will fly up.
digAnsr: b
Ans : (b)
As the ice cube melts completely, the water thus formed will have minimum surface area due to its surface tension. Any state of matter that has a minimum surface area to its volume takes the shape of a sphere. Therefore, as the ice melts, it will take the shape of a sphere.
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Qstn #13
When water droplets merge to form a bigger drop
(a) energy is liberated
(b) energy is absorbed
(c) energy is neither liberated nor absorbed
(d) energy may either be liberated or absorbed depending on the nature of the liquid.
digAnsr: a
Ans : (a)
As the water droplets merge to form a single droplet, the surface area decreases. With this decrease in surface area, the surface energy of the resulting drop also decreases. Therefore, extra energy must be liberated from the drop in accordance with the conservation of energy.
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Qstn #14
The dimension ML^-¹T^-2 can correspond to
(a) moment of a force
(b) surface tension
(c) modulus of elasticity
(d) coefficient of viscosity
digAnsr: c
Ans : (c)
Dimension of modulus of elasticity: `` \frac{{\displaystyle \raisebox{1ex}{$F$}\!\left/ \!\raisebox{-1ex}{$A$}\right.}}{{\displaystyle \raisebox{1ex}{$∆l$}\!\left/ \!\raisebox{-1ex}{$l$}\right.}}=\frac{\left[ML{T}^{-2}\right]}{{L}^{2}}=\left[M{L}^{-1}{T}^{-2}\right]``
Dimension of moment of force: `` FL=\left[ML{T}^{-2}\right]\left[L\right]=\left[M{L}^{2}{T}^{-2}\right]``
Dimension of surface tension: `` \frac{F}{{\displaystyle L}}=\frac{\left[ML{T}^{-2}\right]}{L}=\left[M{T}^{-2}\right]``
Dimension of coefficient of viscosity: `` \frac{FL}{{\displaystyle Av}}=\frac{\left[ML{T}^{-2}\right]\left[L\right]}{\left[{L}^{2}\right]\left[L{T}^{-1}\right]}=\left[M{L}^{-1}{T}^{-1}\right]``
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Qstn #15
Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution in S, the work done in the process is
(a) 8 π r² S
(b) 12 π r² S
(c) 16 π r² S
(d) 24 π r² S
digAnsr: d
Ans : (d)
`` \,\mathrm{\,No\,}.\,\mathrm{\,of\,}\,\mathrm{\,surfaces\,}\,\mathrm{\,of\,}\,\mathrm{\,a\,}\,\mathrm{\,soap\,}\,\mathrm{\,bubble\,}=2``
`` \,\mathrm{\,Increase\,}\,\mathrm{\,in\,}\,\mathrm{\,surface\,}\,\mathrm{\,area\,}=4\,\mathrm{\,\pi \,}(2\,\mathrm{\,r\,}{)}^{2}-4\,\mathrm{\,\pi \,}(\,\mathrm{\,r\,}{)}^{2}=12{\,\mathrm{\,\pi r\,}}^{2}``
`` \,\mathrm{\,Total\,}\,\mathrm{\,increase\,}\,\mathrm{\,in\,}\,\mathrm{\,surface\,}\,\mathrm{\,area\,}=2\times 12{\,\mathrm{\,\pi r\,}}^{2}=24{\,\mathrm{\,\pi r\,}}^{2}``
`` \,\mathrm{\,Work\,}\,\mathrm{\,done\,}=\,\mathrm{\,change\,}\,\mathrm{\,in\,}\,\mathrm{\,surface\,}\,\mathrm{\,energy\,}``
`` =\,\mathrm{\,S\,}\times 24{\,\mathrm{\,\pi r\,}}^{2}=24{\,\mathrm{\,\pi r\,}}^{2}\,\mathrm{\,S\,}``
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Qstn #16
If more air is pushed in a soap bubble, the pressure in it
(a) decreases
(b) increases
(c) remains same
(d) becomes zero.
digAnsr: a
Ans : (a)
Excess pressure inside a bubble is given by: `` P=\frac{4T}{r}``.
When air is pushed into the bubble, it grows in size. Therefore, its radius increases. An increase in size causes the pressure inside the soap bubble to decrease as pressure is inversely proportional to the radius.
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Qstn #17
If two soap bubbles of different radii are connected by a tube,
(a) air flows from bigger bubble to the smaller bubble till the sizes become equal
(b) air flows from bigger bubble to the smaller bubble till the sizes are interchanged
(c) air flows from the smaller bubble to the bigger
(d) there is no flow of air.
digAnsr: c
Ans : (c)
The smaller bubble has a greater inner pressure than the bigger bubble. Air moves from a region of high pressure to a region of low pressure. Therefore, air moves from the smaller to the bigger bubble.
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Qstn #18
Figure shows a capillary tube of radius r dipped into water. If the atmospheric pressure is P₀, the pressure at point A is
(a) P₀
(b)
P0+2Sr
(c)
P0-2Sr
(d)
P0-4SrFigure
digAnsr: c
Ans : (c)

`` \,\mathrm{\,Here\,}:``
`` \,\mathrm{\,Radius\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,tube\,}=\,\mathrm{\,r\,}``
`` \,\mathrm{\,Net\,}\,\mathrm{\,upward\,}\,\mathrm{\,force\,}\,\mathrm{\,due\,}\,\mathrm{\,to\,}\,\mathrm{\,surface\,}\,\mathrm{\,tension\,}=\,\mathrm{\,Scos\theta \,}\times 2\,\mathrm{\,\pi r\,}``
`` \,\mathrm{\,Upward\,}\,\mathrm{\,pressure\,}=\frac{\,\mathrm{\,Scos\theta \,}\times 2\,\mathrm{\,\pi r\,}}{{\,\mathrm{\,\pi r\,}}^{2}}=\frac{2\,\mathrm{\,Scos\theta \,}}{\,\mathrm{\,r\,}}``
`` \,\mathrm{\,Net\,}\,\mathrm{\,downward\,}\,\mathrm{\,pressure\,}\,\mathrm{\,due\,}\,\mathrm{\,to\,}\,\mathrm{\,atmosphere\,}={\,\mathrm{\,P\,}}_{\,\mathrm{\,o\,}}``
`` \Rightarrow \,\mathrm{\,Net\,}\,\mathrm{\,pressure\,}\,\mathrm{\,at\,}\,\mathrm{\,A\,}={\,\mathrm{\,P\,}}_{\,\mathrm{\,o\,}}-\frac{2\,\mathrm{\,Scos\theta \,}}{\,\mathrm{\,r\,}}``
`` \,\mathrm{\,Since\,}\,\mathrm{\,\theta \,}\,\mathrm{\,is\,}\,\mathrm{\,small\,},``
`` \,\mathrm{\,cos\theta \,}\approx 1.``
`` \Rightarrow \,\mathrm{\,Net\,}\,\mathrm{\,pressure\,}={\,\mathrm{\,P\,}}_{\,\mathrm{\,o\,}}-\frac{2\,\mathrm{\,S\,}}{\,\mathrm{\,r\,}}``
`` ``
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Qstn #19
The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is
(a) 4
(b) 2
(c) 1
(d) 0.125
digAnsr: d
Ans : (d)
Let the excess pressure inside the second bubble be P.
∴ Excess pressure inside the first bubble = 2P
Let the radius of the second bubble be R.
Let the radius of the first bubble be x.
`` \,\mathrm{\,Excess\,}\,\mathrm{\,pressure\,}\,\mathrm{\,inside\,}\,\mathrm{\,the\,}2\,\mathrm{\,nd\,}\,\mathrm{\,soap\,}\,\mathrm{\,bubble\,}:``
`` \,\mathrm{\,P\,}=\frac{4\,\mathrm{\,S\,}}{\,\mathrm{\,R\,}}...\left(1\right)``
`` \,\mathrm{\,Excess\,}\,\mathrm{\,pressure\,}\,\mathrm{\,inside\,}\,\mathrm{\,the\,}1\,\mathrm{\,st\,}\,\mathrm{\,soap\,}\,\mathrm{\,bubble\,}:``
`` 2\,\mathrm{\,P\,}=\frac{4\,\mathrm{\,S\,}}{\,\mathrm{\,x\,}}``
`` \,\mathrm{\,From\,}\left(1\right),\,\mathrm{\,we\,}\,\mathrm{\,get\,}:``
`` 2\left(\frac{4\,\mathrm{\,S\,}}{\,\mathrm{\,R\,}}\right)=\frac{4\,\mathrm{\,S\,}}{\,\mathrm{\,x\,}}``
`` \Rightarrow \,\mathrm{\,x\,}=\frac{\,\mathrm{\,R\,}}{2}``
`` \,\mathrm{\,Volume\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,first\,}\,\mathrm{\,bubble\,}=\frac{4}{3}{\,\mathrm{\,\pi x\,}}^{3}``
`` \,\mathrm{\,Volume\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,second\,}\,\mathrm{\,bubble\,}=\frac{4}{3}{\,\mathrm{\,\pi R\,}}^{3}``
`` \Rightarrow \frac{4}{3}{\,\mathrm{\,\pi x\,}}^{3}=\,\mathrm{\,n\,}\frac{4}{3}{\,\mathrm{\,\pi R\,}}^{3}``
`` \Rightarrow {\,\mathrm{\,x\,}}^{3}={\,\mathrm{\,nR\,}}^{3}``
`` \Rightarrow {\left(\frac{\,\mathrm{\,R\,}}{2}\right)}^{3}={\,\mathrm{\,nR\,}}^{3}``
`` \Rightarrow \,\mathrm{\,n\,}=\frac{1}{8}=0.125``
`` ``
`` ``
`` ``
`` ``
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Qstn #20
Which of the following graphs may represent the relation between the capillary rise h and the radius r of the capillary?
Figure
Ans : (c)
`` \,\mathrm{\,The\,}\,\mathrm{\,relationship\,}\,\mathrm{\,between\,}\,\mathrm{\,height\,}\,\mathrm{\,h\,}\,\mathrm{\,and\,}\,\mathrm{\,radius\,}\,\mathrm{\,r\,}\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}:``
`` \,\mathrm{\,h\,}=\frac{2\,\mathrm{\,Scos\theta \,}}{\,\mathrm{\,r\rho g\,}}``
`` \,\mathrm{\,If\,}\,\mathrm{\,S\,},\,\mathrm{\,\theta \,},\,\mathrm{\,\rho \,}\,\mathrm{\,and\,}\,\mathrm{\,g\,}\,\mathrm{\,are\,}\,\mathrm{\,considered\,}\,\mathrm{\,constant\,},\,\mathrm{\,we\,}\,\mathrm{\,have\,}:``
`` \,\mathrm{\,h\,}\propto \frac{1}{\,\mathrm{\,r\,}}``
This equation has the characteristic of a rectangular hyperbola. Therefore, curve
(c) is a rectangular hyperbola.
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Qstn #21
Water rises in a vertical capillary tube up to a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be
(a) 10 cm
(b)
102cm
(c)
10/2cm
(d) none of these
digAnsr: b
Ans : (b)

`` \,\mathrm{\,Given\,}:``
`` \,\mathrm{\,l\,}=10\,\mathrm{\,cm\,}``
`` \,\mathrm{\,\alpha \,}={45}^{0}``
`` \,\mathrm{\,Rise\,}\,\mathrm{\,in\,}\,\mathrm{\,water\,}\,\mathrm{\,level\,}\,\mathrm{\,after\,}\,\mathrm{\,the\,}\,\mathrm{\,tube\,}\,\mathrm{\,is\,}\,\mathrm{\,tilted\,}=h``
`` \Rightarrow \,\mathrm{\,l\,}=h\,\mathrm{\,cos\,}{45}^{0}``
`` \Rightarrow h=\frac{\,\mathrm{\,l\,}}{\,\mathrm{\,cos\,}{45}^{0}}=\frac{10}{\left({\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.}\right)}=10\sqrt{2}\,\mathrm{\,cm\,}``
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Qstn #22
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
(a) 8 cm
(b) 6 cm
(c) 10 cm
(d) 20 cm
digAnsr: d
Ans : (d)
`` \,\mathrm{\,Height\,}\,\mathrm{\,of\,}\,\mathrm{\,water\,}\,\mathrm{\,column\,}\,\mathrm{\,in\,}\,\mathrm{\,capillary\,}\,\mathrm{\,tube\,}\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}:``
`` \,\mathrm{\,h\,}=\frac{2\,\mathrm{\,Tcos\theta \,}}{\,\mathrm{\,r\rho g\,}}``
`` \,\mathrm{\,A\,}\,\mathrm{\,free\,}\,\mathrm{\,falling\,}\,\mathrm{\,elevator\,}\,\mathrm{\,experiences\,}\,\mathrm{\,zero\,}\,\mathrm{\,gravity\,}.``
`` \Rightarrow \,\mathrm{\,h\,}=\frac{2\,\mathrm{\,Tcos\theta \,}}{\,\mathrm{\,r\rho \,}0}=\infty ``
`` \,\mathrm{\,But\,},\,\mathrm{\,h\,}=20\,\mathrm{\,cm\,}\left(given\right)``
`` \,\mathrm{\,Therefore\,},\,\mathrm{\,the\,}\,\mathrm{\,height\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,water\,}\,\mathrm{\,column\,}\,\mathrm{\,will\,}\,\mathrm{\,remain\,}\,\mathrm{\,at\,}\,\mathrm{\,a\,}\,\mathrm{\,maximum\,}\,\mathrm{\,of\,}20\,\mathrm{\,cm\,}.``
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Qstn #23
Viscosity is a property of
(a) liquids only
(b) solids only
(c) solids and liquids only
(d) liquids and gases only.
digAnsr: d
Ans : (d)
Viscosity is one property of fluids. Fluids include both liquids and gases.
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