Tag: properties of matter

Questions Related to properties of matter

Choose the correct statement from the following:

archimedes' principle fluid pressure properties of matter physics

  1. A body will sink in a liquid if its weight is equal to or greater than the weight of the liquid displaced by it

  2. A body will float in a liquid if its weight is equal to or less then the weight of liquid displaced by it

  3. When a body floats in a liquid, the portion of the body above the surface of the liquid is independent of the density of the body relative to that of the liquid

  4. In still air, a hydrogen filled balloon rises up to certain height and then stops rising.

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Correct Option: B,D
Explanation:
According to Archimedes
${ F } _{ b }=$weight of liquid displaced by object
The object floats if ${ F } _{ b }\ge mg$
Weight of liquid displace$\ge $ weight of object
When a body floats the portion immersed or above liquid is dependent on body's density.
The balloon rises till ${ F } _{ b }> mg$. Then stops, since ${ F } _{ b }$ decreases as air gets thin.

Why an iron nail floats on mercury but it sinks in water?

archimedes' principle fluid pressure properties of matter physics

  1. Density of iron is more than that of mercury, but less than that of water.

  2. Density of iron is less than that of mercury, but more than that of water.

  3. Density of iron is less than that of mercury and water

  4. Density of iron is more than that of mercury, water.

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Correct Option: B
Explanation:

This is because density of mercury is more than that of water.
An object floats on a liquid, if its density is lower than that of the liquid. 
The density of iron nail is more than that of the water but less than that of mercury.

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

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

  1. True

  2. False

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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?

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

  1. 1672

  2. 1674

  3. 1676

  4. 1678

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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:-
physics mechanical properties of solids applications of elasticity elastic energy properties of matter

  1. 1000 N

  2. 2000 N

  3. 500 N

  4. 250 N

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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.

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

  1. True

  2. False

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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:-

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

  1. $0.0455 \Omega$

  2. $0.455 \Omega$

  3. $0.91 \Omega$

  4. $0.091 \Omega$

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Correct Option: C

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

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

  1. Remains unchanged

  2. Becomes double

  3. Becomes half

  4. Becomes 1/4 times

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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 

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

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

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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?

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

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

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

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

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

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Correct Option: C