Tag: physics

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Questions Related to physics

Multiple choice various types of barometer fluids physics

The height of a mercury barometer is 75$\mathrm { cm }$ at sealevel and 50$\mathrm { cm }$ at the top of a hill. Ratio of density ofmercury to that of air is $10 ^ { * }$ . The height of the hill is 

  1. 250$\mathrm { m }$
  2. 2.5$\mathrm { km }$
  3. 1.25$\mathrm { km }$
  4. 750$\mathrm { m }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice various types of barometer fluids physics

The value of $\mathrm { g }$ at a place decreases by 2$\%$ . The barometric height of mercury 

  1. Increases by 2$\%$
  2. Decreases by 2$\%$

  3. Remains unchanged

  4. Sometimes increases and so
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Barometric height h = P / (rho * g). If P is constant and rho is constant, h is inversely proportional to g. If g decreases by 2%, h must increase by approximately 2%.

Multiple choice various types of barometer fluids physics

Eight identical spherical mercury drops charged to a potential of $20V$ each are coalesced into a single spherical drop.

  1. The internal Energy of the system remains the same.
  2. The new potential of the drop is $80V$

  3. Internal energy of the system decreases
  4. The potential remains the same i.e., $20V$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Potential of one small drop of mercury, 
$V=\displaystyle\frac{kq}{r}=20V$
Volume of big drop=volume of $8$ small drops
$\displaystyle\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3\Rightarrow =2r$
$Q'=8q$
Potential of big drop,
$\displaystyle V'=\frac{kQ'}{R}=\frac{K\times 8q}{2r}=\frac{4kq}{r}=4\times 20=80V$
Hence, option $B$ is the correct answer.

Multiple choice various types of barometer fluids physics

A cubical block of steel of each side equal 1 is floating on mercury in vessel. The densities of steel and mercury are $ \rho _s and \rho _m $.The height of the block above the mercury level is given by 

  1. $ I \left( 1+\dfrac { \rho _ s }{ \rho _ m } \right) $
  2. $ I \left( 1-\dfrac { \rho _ s }{ \rho _ m } \right) $
  3. $ I \left( 1+\dfrac { \rho _ m }{ \rho _ s } \right) $
  4. $ I \left( 1-\dfrac { \rho _ m }{ \rho _ s} \right) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By Archimedes' principle, the weight of the block equals the weight of the displaced mercury. rho_s * L^3 * g = rho_m * (L^2 * (L-h)) * g, where h is the height above the surface. rho_s * L = rho_m * (L-h). L - h = L * (rho_s / rho_m). h = L * (1 - rho_s / rho_m).

Multiple choice various types of barometer fluids physics

A beaker contining a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the liquid will

  1. Increase

  2. Decrease

  3. Remain constant

  4. First decrease and then increase
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The pressure at depth h in a liquid is P = P_atm + rho * g * h. If the air is pumped out, P_atm decreases, so the total pressure at any depth h also decreases.

Multiple choice various types of barometer fluids physics

A thin tube of uniform cross - section is sealed at both ends. It lies horizontally, the middle $5 \,cm$ containing mercury and the two equal ends containing air at the same pressure P. When the tube is held at an angle $60^o$ with the vertical, the lengths of the air column above and below the mercury are $46$ and $44.5$ cm respectively. Calculate the pressure P, in cm of Hg. (The temperature of the system is kept at $30$ K)

  1. $92.5$ cm of Hg
  2. $75.4$ cm of Hg
  3. $73.0$ cm of Hg
  4. $70.5$ cm of Hg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the ideal gas law PV=nRT and the condition that the mercury column is in equilibrium, the pressure P can be determined by balancing forces at the given angle. The change in air column lengths due to the shift in mercury position allows for solving the system of equations for P. The calculated value aligns with 75.4 cm of Hg.

Multiple choice various types of barometer fluids physics

In a certain region of space, there are n molecules per unit volume. The temperature of the gas T. The pressure of the gas will be: 

  1. $nRT$
  2. $nkT$
  3. $\dfrac{{nT}}{k}$
  4. $\dfrac{{nT}}{R}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ideal gas law is PV = nRT, where n is the number of moles. In terms of number of molecules N, it is PV = NkT, where k is the Boltzmann constant. Dividing by volume V gives P = (N/V)kT, where N/V is the number density n, leading to P = nkT.

Multiple choice various types of barometer fluids physics

How is the barometric height of a simple barometer affected if
(a) its tube is pushed down into the trough of mercury?
(b) its tube is slightly tilted form vertical?
(c) a drop of liquid is inserted inside the tube?

  1. (a) remains unaffected (b) increases (c) decreases

  2. (a) decreases (b) increases (c) decreases

  3. (a) increases (b) remains unaffected (c) increases

  4. (a) remains unaffected (b) remains unaffected (c) decreases
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Below are the answers:
(a) Mercury in the tube adjusts until the weight of the mercury column balances the atmospheric force exerted on the reservoir. High atmospheric pressure places more force on the reservoir, forcing mercury higher in the column. Low pressure allows the mercury to drop to a lower level in the column by lowering the force placed on the reservoir.
When the tube is pushed down into the trough of mercury the height of mercury column above the surface of the bottom surface remains the same. 


(b) When the tube is slightly tilted form vertical, there is no change in the height of the mercury in the tube.

(c) If the vacuum is replaced with a drop, then the drop will exert some pressure on the mercury and there will be inaccurate readings on the barometer. The barometric height is decreased in this case. So, vacuum is present on top of the mercury inside the tube.

Multiple choice various types of barometer fluids physics

Which of the following is not a reason why mercury is preferred as a barometric liquid?

  1. Mercury has high density

  2. Mercury does not wet the glass

  3. Mercury is opaque and shiny

  4. Mercury is poisonous
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

1) It has $13.5$ times higher density than water
2) It doesn't stick to the glass walls of tube like water does.

3) It is opaque and shiny

Multiple choice various types of barometer fluids physics

Atmospheric pressure at a place is $66cm$ of mercury. This place is

  1. $1250m$ above sea level
  2. $1250m$ below sea level
  3. $125m$ above sea level

  4. at the sea level
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Atmospheric pressure at the place is equivalent to that of $66cm$ of mercury.
We know that atmospheric pressure at the sea level is equivalent to that of $76cm$ of mercury.
So, pressure at that place is less by $(76-66)=10cm$ of mercury.
We know that atmospheric pressure decreases by $1cm$ for every $125m$ increase in altitude.
So, the concerned place is $(125 \times 10)m=1250m$ above the sea level.