Tag: applications of elasticity

Questions Related to applications of elasticity

State whether true or false :
The hollow shaft is much stronger than a solid shaft of same mass, same length and same material.

  1. True

  2. False


Correct Option: A
Explanation:

Modulus of elasticity = $\dfrac { stress }{ strain } $     and, stress = $\dfrac { Force }{ Area } $

$\therefore $  Elasticity $\alpha \dfrac { 1 }{ Area } $
As follow shaft, so, elasticity of the follow shaft is more than a solid one. As elasticity measures rigidity. So, hollow shaft is stronger.

In which year Robert Hooke presented his law of elasticity?

  1. 1672

  2. 1674

  3. 1676

  4. 1678


Correct Option: C
Explanation:

In 1676, Robert Hooke presented his law of elasticity, now called Hooke's law.

 A cable that can support a load of 1000 N is cut into equal parts. the maximum load that can be supported by the either part is:-
  1. 1000 N

  2. 2000 N

  3. 500 N

  4. 250 N


Correct Option: A
Explanation:

Maximum load supported by the cable is directly proportional to the breaking stress.

Since,

Breaking stress = F / A

where F is the force and A is the cross-sectional area.

As we see that the breaking stress is independent of the length of the cable. So, if the cable is cut in two equal parts, the maximum load that can be supported by either parts of the cable remain the same as before.

State whether true or false :
The metal used in construction of a bridge should have high Young's modulus.

  1. True

  2. False


Correct Option: A
Explanation:

Young's modulus measures modulus of elasticity of a material. 

Elasticity defines rigidity of the material. 
So, for construction, we need metals which have high elasticity i.e. high young's modulus.

A silver wire of length $10 $ metre and cross-sectional area $10^{-8} m^{2}$ is suspended vertically and a weight of $10 N$ is attached to it. Young's modulus of silver and its resistivity are $7 \times 10^{10} N/m^{2}$ and $1.59 \times 10^{8} N/m^{2}$ \Omega - m$ respectively. The increase in its resistance is equal to:-

  1. $0.0455 \Omega$

  2. $0.455 \Omega$

  3. $0.91 \Omega$

  4. $0.091 \Omega$


Correct Option: C

A steel wire is stretched by 5 kg wt, If the radius of the wire is doubled its Young's modulus

  1. Remains unchanged

  2. Becomes double

  3. Becomes half

  4. Becomes 1/4 times


Correct Option: A

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. $\dfrac { 20 }{ 3 } { m/s }^{ 2 },\dfrac { 100 }{ 3 } N,\dfrac { 50 }{ 3 } N$


Correct Option: C

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. $Y \sqrt {\dfrac{YAe^4}{lm}}$


Correct Option: C

Two wires of equal length and cross section are suspended. their young's modulus are $Y _1$ and $Y _2$ respectively. their equivalent young's modulus of elasticity is

  1. $Y _1+Y _2$

  2. $Y _1Y _2$

  3. $Y _1-Y _2$

  4. $\dfrac{Y _1+Y _2}2$


Correct Option: C

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. $16$


Correct Option: A