Tag: physics

Questions Related to physics

An air bubble rises from the bottom of a deep lake the radius of the air bubble near the surface is 'r'. Choose the appropriate radius of the air bubble.

a) r/2 at depth 30m 

b) r/2 at depth 70m

c) r/3 at depth 140m 

d) r/3 at depth 260m

physics the kinetic model of matter gases and the kinetic theory concept of ideal gas and state equation of ideal gas behaviour of perfect gas and kinetic theory of gases

  1. a,c

  2. a,d

  3. b,c

  4. b,d

Show answer
Correct Option: D
Explanation:

At a depth of h water pressure will be
${P} _{h} = {P} _{a} + \rho gh$                eq(1)
where 
$\rho  =1000 kg/{m}^{3}$
$g  = 9.81 m/{s}^{2} $
$h = \text{depth  of  water  bubble}$
${P} _{a} = {10}^{5}Pa$

initially bubble is below water at h, so
${P} _{1} = {P} _{h}$
finally it rises to surface of lake so
${P} _{2} = {P} _{a}$

we assume that temperature is constant when it is rising from bottom to surface
by ideal gas equation
${P} _{1}{V} _{1} = {P} _{2}{V} _{2}$

volume can be written as $V = \dfrac{4}{3}\pi {r}^{3}$
where r is radius.
${P} _{h} \times \dfrac{4}{3}\pi {r} _{h}^{3} = {P} _{a} \times \dfrac{4}{3}\pi {r} _{s}^{3}$
${r} _{h} = {(\dfrac{{P} _{a}}{{P} _{h}})}^{1/3} r$
${r} _{h} = \dfrac{r}{{(\frac{{P} _{h}}{{P} _{a}})}^{1/3}}$
by eq(1)
${r} _{h} = \dfrac{r}{{(\dfrac{{P} _{a} +  \rho gh}{{P} _{a}})}^{1/3}}$
${r} _{h} = \dfrac{r}{{(1 + 0.0981h)}^{1/3}}$              eq(2)

(a) at depth 30m
h = 30m
put h=30 in eq(2)
${r} _{h} = \dfrac{r}{1.5}$
false

(b) at depth 70m
h = 70m
put h=70 in eq(2)
${r} _{h} = \dfrac{r}{2}$
true

(c) at depth 140m
h = 140m
put h=140 in eq(2)
${r} _{h} = \dfrac{r}{2.4}$
false

(d) at depth 260m
h = 260m
put h=260 in eq(2)
${r} _{h} = \frac{r}{3}$
true

Answer is D.

A barometer reads 75 cm of mercury. When 2.0cm$^{3}$ of air at atmospheric pressure is introduced into space above the mercury level, the volume of the space becomes 50cm$^{3}$. The length by which the mercury column descends is

physics the kinetic model of matter gases and the kinetic theory concept of ideal gas and state equation of ideal gas behaviour of perfect gas and kinetic theory of gases

  1. 3 cm of Hg

  2. 6 cm of Hg

  3. 30 cm of Hg

  4. 10 cm of Hg

Show answer
Correct Option: A
Explanation:

Let the new pressure inside be $P$ after air introduced.

For the air,
$P _1V _1=P _2V _2$
$\implies P(50)=(75)(2)$
$\implies P=3\ cm\  of\ Hg$

Boyle's law is applicable when

a) temperature is constant

b) gas is at high temperature and low pressure

c) the vessel enclosing the gas is good conductor

d) the process is isothermal

physics the kinetic model of matter gases and the kinetic theory concept of ideal gas and state equation of ideal gas behaviour of perfect gas and kinetic theory of gases

  1. a & b

  2. b,c & d

  3. a,b & c

  4. a,b,c & d

Show answer
Correct Option: D
Explanation:

(a) Temperature must be constant to apply boyle's law
(b)From vanderwaal's equation when non idealities of a gas is undertaken then we can apply boyle's only when temperture is high and pressure is low
(c)Vessel enclosing must be a good conductor so there is no any possibilities of adiabatic process
(d) Temperature must be constant therefore, process must be isothermal
Hence all are correct
Hence option(D)

A spring of spring constant $k$ is cut into $3$ equal part find $k$ of each

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $3k$

  2. $\dfrac{k}{3}$

  3. $k$

  4. None of these

Show answer
Correct Option: A

A body of mass 'm' is suspended with an ideal spring of force constant 'k'. The expected change in the position of the body, due to an additional force 'F' acting vertically downwards is 

physics simple harmonic motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $\cfrac { 3F }{ 2K } $

  2. $\cfrac { 2F }{ K } $

  3. $\cfrac { 5F }{ 2K } $

  4. $\cfrac { 4F }{ K } $

Show answer
Correct Option: B

A block of mass m is suddenly released from the top of a string of stiffness constant k.
(i) The maximum compression in the spring will be
(ii) at equilibrium, the compression in the spring will be .......... 

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. 2mg/k, mg/k

  2. mg/k, mg/k

  3. mg/k, 2mg/k

  4. 2mg/k, 2mg/k

Show answer
Correct Option: A

A body of $100 gm$ is attached to a spring balance suspended from the celling of an elevator. If the elevator cable breaks and itt falls freely down, the weight of the body as indicated by the spring balance would be $10gm$.

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $10gm$

  2. $0gm$

  3. $1gm$

  4. $None$

Show answer
Correct Option: A

A block of mass $m$ moving with speed v compresses a spring through distance $x$ before is halved. What is the value of spring constant?

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $\dfrac { 3 m v ^ { 2 } } { 4 x ^ { 2 } }$

  2. $\dfrac { m v ^ { 2 } } { 4 x ^ { 2 } }$

  3. $\dfrac { m v ^ { 2 } } { 2 x ^ { 2 } }$

  4. $\dfrac { 2 m v ^ { 2 } } { x ^ { 2 } }$

Show answer
Correct Option: A
Explanation:

Let the velocity at starting is $v$.

After compression change in velocity $ = \dfrac{v}{2}$
Here, Initial kinetic energy of a block $ = \left( {\dfrac{1}{2}} \right)m{v^2}$
After compression of spring,
Total energy at the point $x$= Kinetic energy of a block +Potential Energy which stored in the spring.
$\begin{array}{l} \left( { \dfrac { 1 }{ 2 }  } \right) m{ v^{ 2 } }=\dfrac { 1 }{ 2 } m{ \left( { \dfrac { v }{ 2 }  } \right) ^{ 2 } }+\dfrac { 1 }{ 2 } k{ v^{ 2 } } \ \dfrac { 1 }{ 2 } k{ v^{ 2 } }=\dfrac { 1 }{ 2 } m{ \left( { \dfrac { v }{ 2 }  } \right) ^{ 2 } }-\dfrac { 1 }{ 2 } \left( { m{ v^{ 2 } } } \right)  \ k{ x^{ 2 } }=m\left( { { v^{ 2 } }-\dfrac { { { v^{ 2 } } } }{ 4 }  } \right)  \ k{ x^{ 2 } }=\dfrac { { 3m{ v^{ ^{ 2 } } } } }{ 4 }  \ \therefore k=\dfrac { { 3m{ v^{ ^{ 2 } } } } }{ { 4{ x^{ 2 } } } }  \end{array}$

A hollow pipe of length $0.8\ m$ is closed at one end. At its open end, a $0.5\ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50\ N$ and the speed of sound is $320\ ms^{-1}$, the mass of the string is

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. $5\ grams$

  2. $10\ grams$

  3. $20\ grams$

  4. $40\ grams$

Show answer
Correct Option: B
Explanation:

Velocity of sound $= c$

$\dfrac{c}{4L} = \dfrac{2v}{l}$

$\Rightarrow \dfrac{320}{4\times 0.8} = \dfrac{1}{5} \sqrt{\dfrac{T}{\mu}}$

$\Rightarrow \mu = 0.02\space kgm^{-1}$

$\Rightarrow m = \mu l = 10\space g $

 

Two blocks are connected to an ideal spring (K = 200 N/m) and placed on a smooth surface. Initially spring is in its natural lenght and blocks are projected as shown. The maximum extension in the spring will be

physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

  1. 30 cm

  2. 25 cm

  3. 20 cm

  4. 15 cm

Show answer
Correct Option: A