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 4

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Qstn #24
The force of viscosity is
(a) electromagnetic
(b) gravitational
(c) nuclear
(d) weak.
digAnsr: a
Ans : (a)
The force of viscosity arises from molecular interaction between different layers of fluids that are in motion. Molecular forces are electromagnetic in nature. Therefore, viscosity must also be electromagnetic.
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Qstn #25
The viscous force acting between two layers of a liquid is given by
FA=-ηdvdz. This F/A may be called
(a) pressure
(b) longitudinal stress
(c) tangential stress
(d) volume stress
digAnsr: c
Ans : (c)
The viscous force acts tangentially between two parallel layers of a liquid. In terms of force on a material, it is analogous to a shearing force.
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Qstn #26
A raindrop falls near the surface of the earth with almost uniform velocity because
(a) its weight is negligible
(b) the force of surface tension balances its weight
(c) the force of viscosity of air balance its weight
(d) the drops are charged and atmospheric electric field balances its weight.
digAnsr: c
Ans : (c)
Air has viscosity. During rainfall, the raindrops acquire acceleration due to gravity. However, the increase in velocity is hindered by the viscous force acting upwards. A gradual balance between the two opposing forces causes the raindrops to attain a terminal velocity, thus, falling with a uniform velocity.
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Qstn #27
A piece of wood is taken deep inside a long column of water and released. It will move up
(a) with a constant upward acceleration
(b) with a decreasing upward acceleration
(c) with a deceleration
(d) with a uniform velocity
digAnsr: b
Ans : (b)
The density of wood is less than that of water.When a piece of wood is immersed deep inside a long column of water and released, it experiences a buoyant force that gives it an upward acceleration. The velocity of wood increases as its motion is accelerated by the buoyant force. However, the viscous drag force acts simultaneously to oppose its upward motion. As a result, the initial acceleration decreases and the wood rises with a decreasing upward acceleration.
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Qstn #28
A solid sphere falls with a terminal velocity of 20 m s^-1 in air. If it is allowed to fall in vacuum,
(a) terminal velocity will be 20 m s^-1
(b) terminal velocity will be less than 20 m s^-1
(c) terminal velocity will be more than 20 m s^-1
(d) there will be no terminal velocity
digAnsr: d
Ans : (d)
In vacuum, no viscous force exists. The sphere therefore, will have constant acceleration because of gravity. An accelerated motion implies that it won't have uniform velocity throughout its motion. In other words, there will be no terminal velocity.
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Qstn #29
A spherical ball is dropped in a long column of a viscous liquid. The speed of the ball as a function of time may be best represented by the graph
(a) A
(b) B
(c) C
(d) D
Figure
digAnsr: b
Ans : (b)
Initially, when the ball starts moving, its velocity is small. Gradually, the velocity of the ball increases due to acceleration caused by gravity. However, as the velocity increases, the viscous force acting on the ball also increases. This force tends to decelerate the ball. Therefore, after reaching a certain maximum velocity, the ball slows down.
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Section : iii

Qstn #1
A student plots a graph from his reading on the determination of Young modulus of a metal wire but forgets to put the labels. the quantities on X and Y-axes may be respectively
(a) weight hung and length increased
(b) stress applied and length increased
(c) stress applied and strain developed
(d) length increased and the weight hung.
Figure
digAnsr: a,b,c,d
Ans : (a),
(b),
(c),
(d)
All options are correct.
(a) When a weight is loaded on a wire, the length of the wire increases. The relationship between weight and length is linear.
(b) When a weight is loaded, it produces stress on the wire. The relationship between stress and increase in length is also linear.
(c) When stress is applied, strain develops. Therefore, both are linearly related.
(d) Since the value of Y for the wire is unknown, X may also be the increase in its length. Nevertheless, they still show the same linear relationship.
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Qstn #2
The properties of a surface are different from those of the bulk liquid because the surface molecules
(a) are smaller than other molecules
(b) acquire charge due to collision from air molecules
(c) find different type of molecules in their range of influence
(d) feel a net force in one direction.
digAnsr: c,d
Ans : (c) &
(d)
(c) The surface molecules acquire air and liquid molecules in their sphere of influence.
(d) The surface molecules have different magnitudes of forces pulling them from the top and the bulk. So, they are affected by a net finite force in one direction.
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Qstn #3
The rise of a liquid in a capillary tube depends on
(a) the material
(b) the length
(c) the outer radius
(d) the inner radius of the tube
digAnsr: a,b,d
Ans : (a),
(b),
(d)
`` \,\mathrm{\,Height\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,liquid\,}\,\mathrm{\,in\,}\,\mathrm{\,the\,}\,\mathrm{\,capillary\,}\,\mathrm{\,tube\,}\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}:``
`` ``
`` \,\mathrm{\,h\,}=\frac{2\,\mathrm{\,Scos\theta \,}}{\,\mathrm{\,r\rho g\,}}``
`` ``
`` \,\mathrm{\,h\,}=\,\mathrm{\,Height\,}``
`` \,\mathrm{\,S\,}=\,\mathrm{\,Surface\,}\,\mathrm{\,tension\,}``
`` \,\mathrm{\,r\,}=\,\mathrm{\,Inner\,}\,\mathrm{\,radius\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,tube\,}``
`` \,\mathrm{\,\rho \,}=\,\mathrm{\,Density\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,liquid\,}``
`` \,\mathrm{\,g\,}=\,\mathrm{\,Acceleration\,}\,\mathrm{\,due\,}\,\mathrm{\,to\,}\,\mathrm{\,gravity\,}``
`` ``
`` a)\,\mathrm{\,\theta \,}\,\mathrm{\,and\,}\,\mathrm{\,\rho \,}\,\mathrm{\,depend\,}\,\mathrm{\,upon\,}\,\mathrm{\,the\,}\,\mathrm{\,material\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,capillary\,}\,\mathrm{\,tube\,}\,\mathrm{\,and\,}\,\mathrm{\,the\,}\,\mathrm{\,liquid\,}.``
`` \,\mathrm{\,b\,})\,\mathrm{\,h\,}\,\mathrm{\,is\,}\,\mathrm{\,dependent\,}\,\mathrm{\,on\,}\,\mathrm{\,the\,}\,\mathrm{\,length\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,tube\,}.\,\mathrm{\,If\,}\,\mathrm{\,the\,}\,\mathrm{\,length\,}\,\mathrm{\,is\,}\,\mathrm{\,insufficient\,},\,\mathrm{\,then\,}\,\mathrm{\,h\,}\,\mathrm{\,will\,}\,\mathrm{\,be\,}\,\mathrm{\,low\,}.``
`` \,\mathrm{\,d\,})\,\mathrm{\,r\,}\,\mathrm{\,is\,}\,\mathrm{\,the\,}\,\mathrm{\,inner\,}\,\mathrm{\,radius\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,tube\,}.``
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Qstn #4
The contact angle between a solid and a liquid is a property of
(a) the material of the solid
(b) the material of the liquid
(c) the shape of the solid
(d) the mass of the solid
digAnsr: a,b
Ans : (a),
(b)
The angle of contact between a solid and a liquid depends upon the molecular forces of both the substances. Therefore, it depends upon the material of the solid and the liquid.
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Qstn #5
A liquid is contained in a vertical tube of semicircular cross section. The contact angle is zero. The force of surface tension on the curved part and on the flat part are in ratio
(a) 1:1
(b) 1:2
(c) π:3
(d) 2:π
digAnsr: c
Ans : (c)

Let the height of the liquid-filled column be L.
Let the radius be denoted by R.
`` \,\mathrm{\,Total\,}\,\mathrm{\,perimeter\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,curved\,}\,\mathrm{\,part\,}=\,\mathrm{\,semi\,}-\,\mathrm{\,circumference\,}\,\mathrm{\,of\,}\,\mathrm{\,upper\,}\,\mathrm{\,area\,}=\,\mathrm{\,\pi r\,}``
`` \,\mathrm{\,Total\,}\,\mathrm{\,surface\,}\,\mathrm{\,tension\,}\,\mathrm{\,force\,}=\pi RS``
`` \,\mathrm{\,Total\,}\,\mathrm{\,perimeter\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,flat\,}\,\mathrm{\,part\,}=2R``
`` \,\mathrm{\,Total\,}\,\mathrm{\,surface\,}\,\mathrm{\,tension\,}\,\mathrm{\,force\,}=2RS``
`` \,\mathrm{\,Ratio\,}\,\mathrm{\,of\,}\,\mathrm{\,curved\,}\,\mathrm{\,surface\,}\,\mathrm{\,force\,}\,\mathrm{\,to\,}\,\mathrm{\,flat\,}\,\mathrm{\,surface\,}\,\mathrm{\,force\,}=\frac{\mathit{\pi }\mathit{R}\mathit{S}}{\mathit{2}\mathit{R}\mathit{S}}=\frac{\,\mathrm{\,\pi \,}}{2}``
`` ``
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Qstn #6
When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary.
(a) The surface tension of the liquid must be zero.
(b) The contact angle must be 90°.
(c) The surface tension may be zero.
(d) The contact angle may be 90°.
digAnsr: c,d
Ans : (c),
(d)
If the liquid level does not rise, it may be assumed that the surface tension is zero or the contact angle is 90°, or both. However, we cannot tell for sure whether the surface tension of the liquid is zero or the contact angle is 0°.
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Qstn #7
A solid sphere moves at a terminal velocity of 20 m s^-1 in air at a place where g = 9.8 m s^-2. The sphere is taken in a gravity-free hall having air at the same pressure and pushed down at a speed of 20 m s^-1.
(a) Its initial acceleration will be 9.8 m s^-2 downward.
(b) It initial acceleration will be 9.8 m s^-2 upward.
(c) The magnitude of acceleration will decrease as the time passes.
(d) It will eventually stop
digAnsr: b,c,d
Ans : (b),
(c),
(d)
(b) There is no gravitational force acting downwards. However, when the starting velocity is 20 m/s, the viscous force, which is directly proportional to velocity, becomes maximum and tends to accelerate the ball upwards.
`` \,\mathrm{\,When\,}\,\mathrm{\,the\,}\,\mathrm{\,ball\,}\,\mathrm{\,fall\,}s\,\mathrm{\,under\,}\,\mathrm{\,gravity\,},``
`` \,\mathrm{\,neglecting\,}\,\mathrm{\,the\,}\,\mathrm{\,density\,}\,\mathrm{\,of\,}\,\mathrm{\,air\,}:``
`` \,\mathrm{\,Mass\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,sphere\,}=m``
`` \,\mathrm{\,Radius\,}=r``
`` \,\mathrm{\,Viscous\,}\,\mathrm{\,drag\,}\,\mathrm{\,coeff\,}.=\eta ``
`` \,\mathrm{\,Terminal\,}\,\mathrm{\,velocity\,}\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}:``
`` mg=6\pi \eta r{v}_{\mathit{T}}``
`` \Rightarrow \frac{6\,\mathrm{\,\pi \,}\eta r{v}_{\mathit{T}}}{m}=g...\left(1\right)``
`` \,\mathrm{\,Now\,},\,\mathrm{\,at\,}\,\mathrm{\,terminal\,}\,\mathrm{\,velocity\,},\,\mathrm{\,the\,}\,\mathrm{\,acceleration\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,ball\,}\,\mathrm{\,due\,}\,\mathrm{\,to\,}\,\mathrm{\,the\,}\,\mathrm{\,viscous\,}\,\mathrm{\,force\,}\,\mathrm{\,is\,}\,\mathrm{\,given\,}\,\mathrm{\,by\,}:``
`` a\mathit{=}\frac{\mathit{6}\mathit{\pi }\mathit{\eta }\mathit{r}{\mathit{v}}_{\mathit{T}}}{\mathit{m}}``
`` \,\mathrm{\,Comparing\,}\,\mathrm{\,equations\,}\left(1\right)\,\mathrm{\,and\,}\left(2\right),\,\mathrm{\,we\,}\,\mathrm{\,find\,}\,\mathrm{\,that\,}:``
`` a\mathit{=}g``
`` ``
Thus, we see that the initial acceleration of the ball will be 9.8 ms`` {}^{-2}``.
(c) The velocity of the ball will decrease with time because of the upward viscous drag. As the force of viscosity is directly proportional to the velocity of the ball, the acceleration due to the viscous force will also decrease.
(d) When all the kinetic energy of the ball is radiated as heat due to the viscous force, the ball comes to rest.
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Section : iv