Volume Stress

Q. Ratio of volumetric stress & volumetric strain is given by
[Take $\left(\Delta P\right)$ to be change in pressure, $V$ as initial volume, $\Delta V$ as change in volume].

1. $-\frac{\Delta V}{V}$
2. $-\frac{V\Delta P}{\Delta V}$
3. $\Delta P$
4. $\frac{\Delta V}{V\Delta P}$

Q. What is volumetric stress?

Q. A hydraulic press contains $0.25{\text{m}}^3$ of oil. Find the percentage decrease in volume of the oil, when it is subjected to a pressure increase $\Delta P=1.6\times {10}^7\text{Pa}$. The bulk modulus of the oil is $B=5.0\times {10}^9\text{Pa}$.

1. $0.32$%
2. $0.64$%
3. $0.82$%
4. $0.96$%

Q.

An external pressure $P$ is applied on a cube at $0^{0}C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :

1. $\frac{P}{3\alpha K}$

2. $\frac{P}{\alpha K}$

3. $\frac{3\alpha }{PK}$

4. $3\alpha PK$

Q. A cylinder of radius $x$ and height $2h$ is to be inscribed in a sphere of radius $R$ centred at $O$ as shown in figure.


i. Evaluate the volume of cylinder in terms of $h$.
ii. The cylinder has maximum volume when $h=?$.

1. i. $V=2\pi h(R^2-h^3)$
   ii. $h=\frac{R}{\sqrt{3}}$
2. i. $V=3\pi h(R^2-h^2)$
   ii. $h=\frac{2R}{\sqrt{3}}$
3. i. $V=2\pi h(R^2-2h^2)$
   ii. $h=\frac{R}{\sqrt{5}}$
4. i. $V=2\pi h(R^2-h^2)$
   ii. $h=\frac{R}{\sqrt{3}}$

Q. Suppose that we have a vernier callipers which does not expand or contract on heating. Such a device is very useful in engineering applications where the dimensions are to be found at different temperatures. One such vernier callipers is used to measure the diameter of a rod at different temperatures as shown in table below. What will be the vernier scale reading (division coinciding) at a temperature of ${50}^{\circ }C$.

Given that $10$ vernier scale divisions coincide with $9$ main scale divisions and $1$ main scale division is equal to $1\text{mm}$.

Temperature T in ${}^{\circ }C$	0	20
Main scale reading	$2.4\text{cm}$	$2.4\text{cm}$
Vernier scale reading	$4^{th}$ division coinciding	$8^{th}$ division coinciding

Q.

The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

Q. A capillary tube of radius $r$ is immersed vertically in a liquid such that liquid rises in it to height $h$ (less than the length of the tube). Mass of liquid in the capillary tube is $m$. If radius of the capillary tube is increased by $50$%, then mass of liquid that will rise in the tube, is

1. $\frac{2}{3}m$
2. $m$
3. $\frac{3}{2}m$
4. $\frac{9}{4}m$

Q. Define stress and explain the types of stress

Q. Ratio of volumetric stress & volumetric strain is given by
[Take $\left(\Delta P\right)$ to be change in pressure, $V$ as initial volume, $\Delta V$ as change in volume].

1. $-\frac{\Delta V}{V}$
2. $\Delta P$
3. $-\frac{V\Delta P}{\Delta V}$
4. $\frac{\Delta V}{V\Delta P}$

Q.

Why poisson ratio of imcompressible substance is 0.5?

Q. Calculate the force needed to punch a 1.46cm diameter hole in a steel plate is 1.27cm thick. The ultimate shear strength of steel is 345N/m2

Q. ${}^{40}K$ isotop of potenssum has half life of $1.37\times {10}^9$ years trn isotop of which is stble. In a particular sample of moon rock, the ration of postassium atoms to argon atoms was found to be 1:7. The age of the rock the rock, assuming that oringinally there was no was no arong present, is

1. $1.37\times {10}^{{}^9}$
2. $5.48\times {10}^{{}^9}$
3. $4.11\times {10}^9$
4. $2.74\times {10}^9$

Q. A mixture of $n_1$ moles of a monoatomic gas and $n_2$ moles of a diatomic gas has $\frac{C_p}{C_v}=\gamma =1.5$. Then,

1. $n_1=2n_2$
2. $2n_1=n_2$
3. $n_1=n_2$
4. $2n_1=3n_2$

Q. An object is resting at the bottom of two strings which are inclined at an angle of ${120}^{\circ }$ with each other. Each string can withstand a tension of 20$N$ The maximum weight of the object that can be sustained without breaking the string is

1. 10$N$
2. 20$N$
3. 20$\sqrt{2}N$
4. 40$N$

Q. At the time of initial tensioning the maximum tensile stress immediately behind the anchorage should not exceed

1. 0.50 Times of ultimate tensile stress
2. 0.60 times of ultimate tensile stress
3. 0.70 times of ulitmate tensile stress
4. 0.80 time of ultimate tensile stress

Q. 'Young's modulus' is defined as the ratio of

1. Hydraulic stress and hydraulic strain
2. Shearing stress and shearing strain
3. Bulk stress and longitudinal strain
4. Tensile stress and longitudinal strain

Q. When a rod is heated but prevent from expanding, stress developed is independent of

1. Material of the rod
2. Rise in temperature
3. Length of rod
4. None of above

Q. The physical quantity which has no dimension is:

1. stress
2. momentum
3. strain
4. angular velocity

Q. Coefficient of linear expansion of a crystal in 3 mutually perpendicular directions are $8.5\times {10}^{-6}{/}^{o}C,10.5\times {10}^{-6}{/}^{o}C,11\times {10}^{-6}{/}^{o}C$. If mass of crystal is $25gm$, its volume at ${60}^{o}C$ is (given density at $0^{o}C$ is $5gm/cc$) :

1. 5.009 cc
2. 4.991 cc
3. 5.9 cc
4. 5.999 cc

Q. hello, , ......i had already asked this but in dint quite understand it coz it was juzt a copy from the reader.....
how does the height of mountain on earth's surface depend upon the shear modulus......y is it not young's modulus?
please answer as soon as possible

Q. If the temperature increase, the modulus of elasticity

1. Increases
2. Decreases
3. Remain constant
4. Becomes zero

Q. Plot the stress-strain graph.

Q. A particle is moving in a circle of radius $R$ in such a way that at any instant the $a_r$ and $a_t$ are equal. If the speed at $t=0$ is $v_0$, the time taken to complete the first revolution is:

1. $\frac{R}{v_0}{e}^{-2\pi }$
2. $v_{0}R$
3. $\frac{R}{v_0}$
4. $\frac{R}{v_0}(1-e^{-2\pi })$

Q. An external pressure $P$ is applied on a cube at $0^{\circ }C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $\alpha$ is its coefficient of linear expansion, suppose we want to bring the cube to its original size by heating. The temperature should be raised by

1. $\frac{P}{\alpha K}$
2. $\frac{P}{3\alpha K}$
3. $3PK\alpha$
4. $\frac{3\alpha }{PK}$

Q. Assertion :Ratio of stress and strain is always constant for a substance. Reason: This ratio is called modulus of elasticity,

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A uniform chain of length $\pi r$ lies inside a smooth semicircular tube AB of radius r. Assuming a slight disturbance to start the chain in motion, the velocity with which it will emerge from the end B of the tube will be

1. $\sqrt{gr(1+\frac{2}{\pi })}$
2. $\sqrt{\pi gr}$
3. $\sqrt{2gr(\frac{2}{\pi }+\frac{\pi }{2})}$
4. $\sqrt{gr(\pi +2)}$

Q. A toy cart is tied the end of an unstrtched string of length a. when revolved, the toy cart moves in a horizontal circle of radius 2a with a time period T. now the toy cart is speeded up until it moves in a horizontal circle of radius 3a with a period T. if Hooke's law holds then

1. T =T
2. $T=\frac{3}{2}$
3. $T=\sqrt{\frac{3}{2}}T$
4. $T=\frac{\sqrt{3}}{2}T$

Q. In a capillary tube of radius 'R', a straight thin metal wire of radius 'r' (R > r) is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is [T = surface tension of water, $\rho$ = density of water, g = gravitational acceleration]

1. $\frac{T}{(R+r)\rho g}$
2. $\frac{R\rho g}{2T}$
3. $\frac{2T}{(R-r)\rho g}$
4. $\frac{(R-r)\rho g}{T}$

Q.

A uniform pressure P is exerted on all sides of a solid cube at temperature $t^{\circ }C$. By what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube is $\alpha$ and the bulk modulus is $\beta$.

1. $\frac{P}{\alpha \beta }$

2. $\frac{P\alpha }{\beta }$

3. $\frac{P\beta }{\alpha }$

4. $\frac{\alpha \beta }{P}$