Springs

Q.

The surface tension of water is 72 dyne/cm. Convert it in SI unit.

Q.

What is torsional stress?

Q.

Why is Hookes Law negative?

Q.

Among the following, which is the least elastic?

1. Steel

2. Iron

3. Copper

4. Rubber

Q. Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radis 0.06 m. Each sping has a natural lenght of $0.006\pi m$ and force constant of $0.1N/m$. Initially both the balls are displaced by an angle $\theta =\pi /6$ radian with respect to the diameter PQ of the circle and released from rest. The frequency of oscillation of the ball B is

1. $\pi Hz$
2. $\frac{1}{\pi }Hz$
3. $2\pi Hz$
4. equal to frequency of oscillation of ball A

Q. If the tension in a stretched string fixed at both ends is increased by $21$%, the fundamental frequency is found to be changed by $15$ Hz. Then, the

1. original frequency is $150$ Hz.
2. velocity of propagation of the transverse wave along the string increases by $5$%
3. velocity of propagation of the transverse wave along the string increases by $10$%
4. fundamental wavelength on the string does not change

Q. A tuning fork of frequency $512Hz$ is vibrated with a sonometer wire and $6$ beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is

1. $506Hz$
2. $512Hz$
3. $518Hz$
4. $524Hz$

Q. A cable is replaced by another one of same length and material, but twice the diameter. How does this affect the maximum load it can support without exceeding the elastic limit ?
(Mass of cable is negligible)

1. Wire can support 8 times the original load
2. Wire can support 16 times the original load
3. Wire can support 6 times the original load
4. Wire can support 4 times the original load

Q.

When you climb up the stairs, your potential energy increases.

1. True
2. False

Q.

The Young's modulus of the material of a wire is $6\times {10}^{12}N/m^2$ and there is no transverse(lateral) strain in it, then its modulus of rigidity will be

1. 

2. 

3. None of the above

4. 

Q. Strain energy of a solid body due to a gradually applied load is equal to:
(Consider the cross-sectional area of the body to be uniform throughout)

1. $0.5\times \text{load}\times \text{extension}$
2. $0.5\times \frac{YA}{L}\times (\Delta L{)}^2$
3. Work done by load
4. $0.5\times \text{stress}\times \text{strain}\times \text{volume}$

Q. Two springs $P$ and $Q$ of force constants $k_P$ and $k_Q(k_Q=\frac{k_P}{2})$ are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$, then the energy stored in $P$ is

1. $\frac{E}{8}$
2. $E$
3. $\frac{E}{4}$
4. $\frac{E}{2}$

Q.

A crowbar is of length $3m$. Where should the ful­crum be placed along the length of the crowbar so that a boulder of $9k{g}_{wt}$, be lifted with it by applying an effort of $10N$? $(g=10m{s}^{-2})$.

Q. A load suspended by a massless spring produces an extension of $x\text{cm}$ in equilibrium. When it is cut into two unequal parts, the same load produces an extension of $7.5\text{cm}$ when suspended by the larger part of length $60\text{cm}$. When it is suspended by the smaller part, the extension is $5.0\text{cm}$. Then

1. $x=12.5\text{cm}$
2. $x=3.0\text{cm}$
3. The original length of the spring is $90\text{cm}$.
4. The original length of the spring is $80\text{cm}$

Q.

In which manner does current or voltage vary in an analog signal with time?

Q.

Name the energy possessed by a flower pot placed on the rooftop of a building.

Q.

If the breaking force for a given wire is F, then the breaking force of two wires of the same magnitude will be _____.

Q. A rod of lenght L and diameter d is subjected to a tensile load P. Which of the following is sufficient to calculte the resulting change in diameter?

1. Young's modulus
2. Shear modulus
3. Poission's ratio
4. Both Young's modulus and shear modulus

Q.

Three point charges $Q_1$, $Q_2$and $Q_3$ in that order are placed equally spaced along a straight line. $Q_2$and $Q_3$ are equal in magnitude but opposite in sign. If the net force on $Q_3$ is zero, the value of $Q_1$ is :

1. $Q_1=\sqrt{2}\left|Q_3\right|$
2. $Q_1=\left|Q_3\right|$
3. $Q_1=2\left|Q_3\right|$
4. $Q_1=4\left|Q_3\right|$

Q. A wire of a certain length and radius is stretched by a force $F$. If the length of the wire and radius are both doubled, then the value of Young's modulus $Y$ will become

1. $2$ times
2. $4$ times
3. Remains same
4. Half

Q.

What is potential energy?

Q. A spring of spring constant 2k and length L is split in to two equal parts. What is the effective spring constant, if both are connected in parallel

1. 2k
2. 4k
3. k
4. k/2

Q. Two $L$ shaped wires are kept over each other as shown. The wire on the left is fixed and the wire on the right is movable on the left wire without any friction. The whole system in a horizontal plane. Now we make a soap film of surface tension $0.1\text{N/m}$ in between the wires such that it covers the common quadrilateral area. If the right wire has a mass of $250\text{gm}$, what is its initial acceleration (in ${\text{m/s}}^2$ ) on being released?

Q. A uniform heavy rod of weight W, cross-sectional area A and length L is hanging from a fixed support. Young modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.

1. 3
2. 4
3. 1
4. 2

Q. A block of mass $m$ held touching the upper end of a light spring of force constant $K$ as shown in the figure. Find the maximum potential energy stored in the spring if the block is released suddenly on the spring.

1. $\frac{m^2{g}^2}{k}$
2. $\frac{2m^2{g}^2}{k}$
3. $\frac{4m^2{g}^2}{k}$
4. $\frac{m^2{g}^2}{2k}$

Q. A mass of $2\text{kg}$ is released from a height of $40\text{cm}$ on a spring whose force constant of $1960\text{N/m}$. The maximum compression in the spring is

1. $10\text{cm}$
2. $1\text{cm}$
3. $20\text{cm}$
4. $5\text{cm}$

Q. If a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain $\sigma$ and modulus of elasticity $Y$ is :-

1. $\frac{Y\sigma }{2}$
2. $\frac{Y{\sigma }^2}{2}$
3. $\frac{2Y{\sigma }^2}{2}$
4. $\frac{Y^2\sigma }{2}$

Q.

A block of mass $5kg$ is connected to a vertical spring, as a result, the spring elongates by $4cm$. If another block of mass $2kg$ is attached to the block of mass $5kg$, determine the further elongation in spring.

Q. Select the correct alternative $\left(s\right)$
a) Elastic forces are always conservative
b) Elastic forces are not always conservative
c) Elastic forces are conservative only when Hooke's law is obeyed
d) Elastic forces may be conservative even when Hooke's law is not obeyed

1. $a,d$
2. $b,c$
3. $b,d$
4. $a,c$

Q. A spring of spring constant $k$ is cut into two pieces such that their lengths are in the ratio $1:2,$ then the force constant of the bigger piece will be

1. $\frac{k}{2}$
2. $2k$
3. $\frac{3k}{2}$
4. $3k$