Tag: elastic energy

Quizzes (0) Questions (143)

Questions Related to elastic energy

Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

In the system shown in figure pulley is smooth. String is massless and inextensible. The acceleration of the system a, tensions ${T} _{1}\ and {T} _{1}\left (g=10{m/s}^{2}\right)$ are 

  1. $\dfrac { 20 }{ 3 } { m/s }^{ 2 },\dfrac { 50 }{ 3 } N,\dfrac { 60 }{ 3 } N$

  2. $\dfrac { 10 }{ 3 } { m/s }^{ 2 },\dfrac { 100 }{ 3 } N,\dfrac { 60 }{ 3 } N$

  3. $\dfrac { 20 }{ 3 } { m/s }^{ 2 },\dfrac { 100 }{ 3 } N,\dfrac { 60 }{ 3 } N$

  4. $\dfrac { 20 }{ 3 } { m/s }^{ 2 },\dfrac { 100 }{ 3 } N,\dfrac { 50 }{ 3 } N$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

A stone of mass 'm' s projected from a rubber catapult of length 'l' and cross-sectional area A stretched by an amount 'e'. If Y be the young's modulus of rubber then the velocity of projection of stone?

  1. $Y \sqrt {\dfrac{Ae^2}{lm}}$

  2. $ \sqrt {\dfrac{Ae^2}{lm}}$

  3. $Y \sqrt {\dfrac{YAe^2}{lm}}$

  4. $Y \sqrt {\dfrac{YAe^4}{lm}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

In the Young's double slit experiment the intestines at two points $P _{1}$ and $P _{2}$ on the screen are respectively $I _{1}$ and $I _{2}$. If $P _{1}$ is located at the centre of bright fringe and $P _{2}$ is located at a distance equal to a quarter of fringe width from $P _{1}$, then $I _{1}/I _{2}$ is 

  1. $2$

  2. $1/2$

  3. $4$

  4. $16$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Intensity I = 4 * I0 * cos^2(phi/2). At the center (P1), phi = 0, so I1 = 4 * I0. At a distance of quarter fringe width (P2), the path difference is lambda/4, so phase difference phi = 2 * pi * (lambda/4) / lambda = pi/2. I2 = 4 * I0 * cos^2(pi/4) = 4 * I0 * (1/2) = 2 * I0. Therefore, I1/I2 = 4 * I0 / 2 * I0 = 2.

Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

An Indian rubber cord $L$ metre long and area of cross-section $A$ meter$^2$ is suspended vertically. Density of rubber is $\rho \ kg/$ meter$^3$ and Young's modulus of rubber is $Y$ Newton/metre$^2$. If the cord extends by $l$ metre under its own weight, then extension $l$ is:

  1. $\dfrac{L^2 \rho g}{Y}$

  2. $\dfrac{L^2 \rho g}{2Y}$

  3. $\dfrac{L^2 \rho g}{4Y}$

  4. $\dfrac{Y}{L^2 \rho g}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A small differential element $dx$ at distance $x$ from the bottom of chord

Force acting on this element $ = \dfrac{M}{L} \times x \times g$
If extension  in this element is $dl$
Then
$\begin{array}{l} \dfrac { { dl } }{ { dx } } =\dfrac { f }{ { Ay } } =\dfrac { { Mg } }{ { LAy } } x \ \int  _{ 0 }^{ l }{ dl }=\dfrac { { Mg } }{ { LAy } } \int  _{ 0 }^{ l }{ xdx } \ l=\dfrac { { Mg{ L^{ 2 } } } }{ { 2LAy } } =\dfrac { { Mgl } }{ { 2Ay } }  \ If\, density\, is\, f\, then, \ \rho =\dfrac { m }{ { AL } }  \ So,\, l=\dfrac { { \rho g{ L^{ 2 } } } }{ { 2y } }  \ Hence\, option\, B\, is\, the\, correct\, answer. \end{array}$

Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

A breaking stress of a material is ${ 10 }^{ 6 }N/{ m }^{ 2 }$ If density of material is $3\times 10^{ 3 }kg/{ m }^{ 3 }$, what should be the length of the material so that its breaks by it own weight?

  1. 43.3 m

  2. 23.3 m

  3. 13.3 m

  4. 33.3 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The wire breaks under its own weight when the stress at the top equals the breaking stress. Stress = (m * g) / A = (rho * V * g) / A = rho * L * g. Therefore, L = breaking_stress / (rho * g) = 10^6 / (3e3 * 10) = 10^6 / 3e4 = 33.33 m.

Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

Two wire of same radius and length are subjected to the same load, One wire is of steel and the other is copper. If Young's modulus of steel is twice that of copper, then the ratio of elastic energy stored per unit volume of steel to that of copper wire is

  1. $2:1$

  2. $1:2$

  3. $1:4$

  4. $4:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
${ Y } _{ S }=2{ Y } _{ C }$, then the ratio of elastic energy stored per unit volume.
$E=\dfrac { 1 }{ 2 } \dfrac { { YL }^{ 2 }\alpha  }{ L } $
or,  $\dfrac { E }{ { l }^{ 2 }\alpha  } =\dfrac { 1 }{ 2 } \dfrac { Y }{ L } $
Since same length and same radius.
$\dfrac { { E }^{ 1 } }{ { l }^{ 2 }\alpha  } =\dfrac { 1 }{ 2 } \dfrac { { Y } _{ C } }{ L } $
$\dfrac { { E }^{ 11 } }{ { l }^{ 2 }\alpha  } =\dfrac { 1 }{ 2 } \times \dfrac { 2{ Y } _{ C } }{ L } $
$\dfrac { { E }^{ 1 } }{ { E }^{ 11 } } =\dfrac { 1 }{ 2 } $.