Shear Stress

Q. A steel rod 2.0 m long has a cross-sectional area of 0.30 cm2. The rod is now hung by one endfrom a support structure, and a 550 kg milling machine is hung from the rods lower end. Determine the stress, the strain, and the elongation of the rod

Q. 85. A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long . Those at each end are of copper and the middle one is of iron . Determine the ratio of their diameters if each is to have the same tension .

Q. 65.A solid cylinder is wrapped with a string on an inclined plane as shown in figure then the friction force acting between cylinder plane is

Q. An elevator cable is to have a maximum stress of 7x10^7 N/m^2 to allow for appropriate safety factors. Its maximum upward acceleration is 1.5 m/s^2. If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross-section of the cable should be

Q. 27. A vertical hanging bar of length l & mass m per unit lenght carries a load of Mass M at lower end, its upper end is clamped to a rigit support. The tensile stress a distance x from support is ( A= area of cross section of bar) 1) Mg + mg (1-x)/A 2) Mg/A 3) Mg + mgl/A 4) (M+m)gx/Al

Q. A heavy particle hanging from a string of length is projected horizontally with speed \sqrt{gl}. Find the speed of the particle at the point where the tensionin the string equals weight of the particle.

Q. One end of a uniform rod of mass m, and cross-sectional area A is hung from a ceiling. The otherend of the bar is supporting mass mo. The stressof the midpoint is

Q. 25. A block of mass M moving with speed u collides elastically with block B of mass m which is connected to block C of mass m with a spring. When the compression in spring is maximum, the velocity of block C with respect to block A is. Neglect friction.

Q. Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 10⁷ Pa? Assume that each rivet is to carry one quarter of the load.

Q. 46.Two inclined planes forming angles 30^° and 45^° are hinged together .A weightless pulley is attached to the hinge.Two bodies A and B each of weight 1kg are linked by rope passing over the pulley.1. Find acceleration of system and tension of rope neglecting the friction. 2.Solve the problem if the coefficient of friction between the two bodies are 0.1

Q. A copper cube 0.30m on a side is subjectedto a shearing force of F 6.0x 10^° N. Assumingthat the shear modulus for copper is4.2x101^° N/m2. The angle through, which thecube shear is (approximately)

Q. a mass spring system oscillates such that the mass moves on a rough surface with coefficient of friction u . it is compressed by a dis†an ce a fom its normal length and on being released it moves to a dis†an ce b from equilibrium position .the decrease in amplitude for one half cycle(-a to b) is

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 what is the shearing stress on PQ

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Q. 57. Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are frictionless. Find the acceleration of the mass M and tension in the string.

Q. 7.The frictional force arcing on 1kg block is

Q. what is the formula of †an gential or shearing stress

Q.

There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

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Q. ) The upper end of wire of diameter 12 mm and lengthtm is ciamped and its other ond is twisted throughan angle of 30 Tha angle of shear is(1) 18(3) 0.18^° (2) 36(4) 0.36

Q.

A uniform wire of length 1m and radius 1mm is twisted by an angle 30degree. Find the shear strain (in degree) produced in it.

Q. 92.A monkey is sitting on a tree limb. The limb exerts a normal force of 48N and a frictional force of 20N. Find the magnitude of the total force exerted by the limb of the monkey.

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. A cord is used to lower vertically a block of mass M by a distance d with constant downward accelaration g/4 . Work done by the cord on the block is

Q. Solve this:

Q12. A block A of mass m₁ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m₂ is suspended. The coefficient of kinetic friction between the block and the table is ${\mathrm{\mu }}_{\mathrm{k}}$. When the block A is sliding on the table, the tension in the string is :-

$$\begin{gathered} \left(1\right)\frac{\left({\mathrm{m}}_2-{\mathrm{\mu }}_{\mathrm{k}}{\mathrm{m}}_1\right)\mathrm{g}}{\left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}\left(2\right)\frac{{\displaystyle {\mathrm{m}}_1{\mathrm{m}}_2\left(1+{\mathrm{\mu }}_{\mathrm{k}}\right)\mathrm{g}}}{{\displaystyle \left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}} \\ \left(3\right)\frac{{\displaystyle {\mathrm{m}}_1{\mathrm{m}}_2\left(1-{\mathrm{\mu }}_{\mathrm{k}}\right)\mathrm{g}}}{{\displaystyle \left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}}\left(4\right)\frac{{\displaystyle \left({\mathrm{m}}_2+{\mathrm{\mu }}_{\mathrm{k}}{\mathrm{m}}_1\right)\mathrm{g}}}{{\displaystyle \left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}} \end{gathered}$$

Q. A mass- spring system oscillates such that the mass moves on a rough surface having coefficient of friction μ. It is compressed by a dis†an ce a from its normal length and, on being released, it moves to a dis†an ce b from its equilibrium position. The decrease in amplitude for one half-cycle (-ato b) is

Q. differentiate force and weight

Q. A shear stress gets developed when the force is applied perpendicular to cross section.

1. True
2. False

Q. One end of uniform rod of mass M and cross sectional area A is suspended from rigid support and an equal mass M is suspended at the other end . What is the stress at the mid point?

Q. 6.A load of 1kg weight is attached to one end of a steel wire of cross sectional area 3mm2 and Youngs modulus 10power11N/m2.The other end is suspended vertically from a hook on a wall then the load is pulled horizontally and released. when the load passes its lowest position the fractional change in length is
(g=10m/s2)

Q. A cube of aluminium each side 4cm is subjected to a tangential or shear force . the top face of the cube is sheared through 0.012cm with respect to the bottom face ?
FIND a. shearing strain
b. shearing stress
c. shearing force
n=2x10^​11 dyes/ cm²