Shear Stress

Q. In Millikan's oil drop experiment, what is the viscous force acting on an uncharged drop of radius $2.0\times {10}^{-5}\text{m}$ and density $1.2\times {10}^3{\text{kgm}}^{-3}$. Take viscosity of liquid $=1.8\times {10}^{-5}{\text{Pasm}}^{-2}.$
(Neglect buoyancy due to air).

1. $1.8\times {10}^{-10}\text{N}$
2. $3.8\times {10}^{-11}\text{N}$
3. $5.8\times {10}^{-10}\text{N}$
4. $4\times {10}^{-10}\text{N}$

Q. A block of gelatin is $60mm$ by $60mm$ by $20mm$ when unstressed. A force of $0.245N$ is applied tangentially to the upper surface, causing a $5mm$ displacement relative to the lower surface. Following observations are made regarding the block.
$\left(i\right)$ the shearing stress develop on surface is $68.1pa$
$\left(ii\right)$ the shearing strain develop on surface is $0.25$
$\left(iii\right)$ the shear modulus of material is $274.4\frac{N}{M^2}$

1. 
   only statement $\left(i\right)$ and $\left(iii\right)$ are correct
   
2. 
   only statement $\left(i\right)$ and $\left(iii\right)$ are correct
   
3. 
   
   all the statements are correct
   
4. 
   only statement $\left(i\right)$ and $\left(ii\right)$ are correct
   

Q. A bar magnet is cut into two equal halves by a plane parallel to the magnetic axis. From the given following physical quantities, which remains unchanged is

1. pole strength
2. magnetic moment
3. intensity of magnetisation
4. moment of inertia

Q. A tie member of truss consist of two ISA $90\times 90\times 8$ placed back to back connected to a gusset plate of $10mm$, has to carry a factored load of $250kN$. The grade of steel is Fe410 and one of the shear plane passes through thread.The number of bolts of diameter $18mm$ of $4.6$ class bolts required are _______.(Take $k_b=0.5$)

1. 4

Q. Force produces a change in the shape of the body without changing its volume, strain produced is called what the (longitudinal strain , shearing strain, volumetric strain, normal stress? Give reason

Q.

The breaking stress of a material is 108N/m, density of material is 3000kg/m3
. Find the greatest
length of wire that could hang vertically without breaking. (Pause the video and solve without
looking at the solution).

Q.

A metal ring of initial radius $r$ and cross-sectional area $A$ is fitted onto a wooden disc of radius $R>r$ .if Youngs modulus of metal is $Y$ then tension in the ring is:

Q. Assume that if the shear stress in steel exceeds about $4.00\times {10}^8{\text{N/m}}^2$, the steel ruptures. If the shearing force necessary to rupture a steel bolt of diameter $1.00\text{cm}$ is $x\times {10}^4\text{N}$, then $x$ is
[Take $\pi =3.14$ and answer upto two decimal places]

Q. Aforce of 10^6 /m^2 is required for breaking a material .if the density of material is 3000 kg/m^2 , then what should be the minimum length of wire made of the same material so that it breaks by its own weight

Q. The upper end of a wire (diameter $12\text{mm}$ and length $1\text{m}$) is clamped and its other end is twisted through an angle of ${30}^{\circ }$. The angle of shear is

1. ${18}^{\circ }$
2. ${0.18}^{\circ }$
3. ${36}^{\circ }$
4. ${0.36}^{\circ }$

Q. The magnetic field at the centre of a circular coil of radius $r$ is $\pi$ times that due to a long straight wire at a distance $r$ from it, for equal currents. The following figures show three cases: In all cases the circular part has radius $r$ and straight ones are infinitely long. For same current, the magnetic field $B$ at the centre $P$ in cases $1,2,3$ has the ratio

1. $(-\frac{\pi }{2}-1):(\frac{\pi }{2}+\frac{1}{4}):(\frac{3\pi }{4}+\frac{1}{2})$
2. $(-\frac{\pi }{2}):\left(\frac{\pi }{2}\right):(\frac{3\pi }{4}-\frac{1}{2})$
3. $-\frac{\pi }{2}:\frac{\pi }{2}:3\frac{\pi }{4}$
4. $(-\frac{\pi }{2}+1):(\frac{\pi }{2}+1):(\frac{3\pi }{4}+\frac{1}{2})$

Q. Two short magnets each of moment $M$ are placed one over the other at right angles. The resultant magnetic induction at a point $\text{P}$ that lies at a distance $d$ from the common centre is-

1. $\left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{d^3}$
2. $\left(\frac{{\mu }_0}{4\pi }\right)\frac{3M}{d^3}$
3. $\sqrt{3}\times \left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{d^3}$
4. $\sqrt{5}\times \left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{d^3}$
   
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Q.

The diagram shows the change x in length of a thin uniform wire caused by the application of stress F, at two different temperatures $T_1$ and $T_2$. The variations shown suggest that:

1. $T_1<T_2$

2. $T_1>T_2$

3. $T_1=T_2$

4. None

Q.

The length of the metallic wire is $l_1$ when the tension in it is $T_1$ It is $l_2$ when the tension is $T_2$. The original length of the wire will be:

1. $\frac{\left(l_1+l_2\right)}{2}$

2. $\frac{\left(T_1{l}_1-T_2{l}_2\right)}{\left(T_2-T_1\right)}$

3. $\frac{\left(T_2{l}_1+T_1{l}_2\right)}{\left(T_2+T_1\right)}$

4. $\frac{\left(T_2{l}_1-T_1{l}_2\right)}{\left(T_2-T_1\right)}$

Q. A fluid (Prandtl number $Pr=1$) at $500K$ flows over a flat plate of $1.5m$ length, maintained at $300K$. The velocity of the fluid is $10m/s.$ Assuming kinematic viscosity, $v=30\times {10}^{-6}{m}^2/s,$ the thermal boundary layer thickness $\left(inmm\right)$ at $0.5m$ from the leading edge is

Q. A smooth two dimensional flat plate is exposed to a wind velocity of $80kmph$. Laminar boundary layer exists upto Reynolds no.of flow equal to $3\times {10}^5$. The kinematic viscosity of wind is $1.5\times {10}^{-5}{m}^2/sec$. The maximum thickness of laminar boundary layer (in mm) is ___.

1. 1.75

Q. Breaking stress depends on

1. length of wire
2. area of cross-section of wire
3. Both (a) and (b)
4. independent of length and area of cross-section

Q.

A spring with natural length$l_0$ has a tension $T_1$ when its length is $l_1$ and the tension is $T_2$ when its length is$l_2$. The natural length of spring will be:

1. $\frac{T_1{l}_2-T_2{l}_1}{l_1-l_2}$

2. $\frac{T_2{l}_1-T_1{l}_2}{T_2-T_1}$

3. $\frac{T_2{l}_2-T_1{l}_1}{T_1-T_2}$

4. $\frac{T_2{l}_1-T_1{l}_2}{T_2+T_1}$

Q. What is shear stress?

Q. Assume that if the shear stress in steel exceeds about $4.00\times {10}^8{\text{N/m}}^2$, the steel ruptures. If the shearing force necessary to rupture a steel bolt of diameter $1.00\text{cm}$ is $n\pi \times {10}^4\text{N}$, then find $n$

Q. A continuous beam of span $12$ $m$ is subjected to uniformly distributed load. The minimum effective depth of beam required to check deflection of the beam, when modification factor for tension steel is $0.9$ is:

1. $520$ $mm$
2. $620$ $mm$
3. $670$ $mm$
4. $580$ $mm$

Q. The drawing shows two cylinders. They are identical in all respects, except that B is hollow. In a setup like that in the figure, identical forces are applied to the right end of each cylinder while the left end is fixed.

1. The elongation of A is more than that of B.
2. The elongation of B is more than that of A.
3. The energy stored in B is more than that in A.
4. The energy stored in A is more than that in B.

Q. A furnace has a two layered wall as shown. Each layer has the same area of cross -section. The temperature $\theta$ at the interface of two layers can be reduced by (keeping other parameters constant)

1. increasing the thermal conductivity of outer layer
2. decreasing the thermal conductivity of inner layer
3. by increasing the thickness of the inner layer
4. by decreasing the thickness of the outer layer

Q.

what is the dimensional formula of co-efficient of shear modulus?

Q. A short bar magnet of moment $4{\text{Am}}^2$ is placed in the magnetic merdian with its south-pole pointing geographic north. The distance between two null points is found to be $20\text{cm}$.

$\left(ii\right)$If the magnet is turned through ${90}^{\circ }$ , the resultant field at the location of the null point will be.

1. $2\sqrt{5}\times {10}^{-4}\text{T}$
2. $4\sqrt{5}\times {10}^{-4}\text{T}$
3. $3\sqrt{5}\times {10}^{-4}\text{T}$
4. $8\sqrt{5}\times {10}^{-4}\text{T}$

Q. The ratio of shear stress to shear strain is ....................

1. Poisson's ratio
2. Young's modulus
3. Bulk modulus
4. Rigidity modulus

Q. Find out longitudinal stress and tangential stress on the given fixed block

Q. A bar of cross section $A$ is subjected to equal and opposite tensile forces $F$ at its ends. Consider the plane through the bar making an angle $\theta$ with a plane at right angles to the bar shown in the figure.
Shearing stress at this plane, in terms of $F,A$ and $\theta$

1. $Fsin\theta$
2. $\frac{Fsi{n}^2\theta }{A}$
3. $\frac{Fsin\theta cos\theta }{A}$
4. $\frac{Fco{s}^2\theta }{A}$

Q. A cube of side $40mm$ has its upper face displaced by $0.1mm$ by a tangential force of $8kN$. The shearing modulus of cube is

1. $2\times {10}^{9}N{m}^{-2}$
2. $4\times {10}^{9}N{m}^{-2}$
3. $8\times {10}^{9}N{m}^{-2}$
4. $16\times {10}^{9}N{m}^{-2}$

Q. A bar is subjected to equal and opposite forces as shown in the figure. PQRS is a plane making angle $\theta$ with the cross-section of the bar. If the area of cross-section be ‘A’, then when is the shearing stress maximum

1. 
2. 
3. 
4.