Tag: physics

Questions Related to physics

A large cylindrical tank has a hole of area $A$ at its bottom and water is poured into the tank through a tube of cross-section area $A$ ejecting water at the speed $v$. Which of the following is true?

physics pressure in fluids and atmospheric pressure examples of hydraulic press applications of pascal's law pascal's law and its applications

  1. Water level in tank keeps on rising

  2. No water can be stored in the tank

  3. Water level will rise to height $v^{2}/2g$ and then stop

  4. The water level will be oscillating

Show answer
Correct Option: C
Explanation:

In the beginning ,the water escaping the vessel at the rate $\sqrt{2gh}$ and filling it at the rate of $vA$


So the rate of change in the water level of the vessel at any instant is 
($v-\sqrt{2gh})A$ 
where  'h' is the instantaneous height 

Since h is quite small in the beginning, the water is escaping the vessel at a slow rate but filling at a much larger rate as such    ($v-\sqrt{2gh})A$  ,is positive  (increase in water level)

soon after the filling of water  occurs, the height increases and the rate of escape become larger 
But when the rate =rate of filling ,then an equilibrium state is reached and there is no net change  in the height of the water 

the equilibrium is reached when ($v-\sqrt{2gh})A$ =0  $\rightarrow$  $h=\dfrac{v^2}{2g}$

The minute hand of the clock is 4 cm long. The average velocity of the tip of the minute hand between 11:00 am to 11:30 am is:

lorentz transformation and muon experiment option a: relativity physics

  1. $1.5\times { 10 }^{ -5 }{ m }/{ s }$

  2. $4.4\times { 10 }^{ -5 }{ m }/{ s }$

  3. $1.8\times { 10 }^{ -6 }{ m }/{ s }$

  4. $3.5\times { 10 }^{ -6 }{ m }/{ s }$

Show answer
Correct Option: B
Explanation:

Average velocity $ = \dfrac{Total \; Displacement}{Total \; Time}$


$ = \dfrac{  2\times 0.04}{30 \times 60} = 4.44 \times 10^{-5} \;m/s$

Suppose a new planet is discovered, which revolves around the sun (i.e. it is a part of our solar system). If its lies between saturn and Jupitar, its time period of revolution would be 

lorentz transformation and muon experiment option a: relativity physics

  1. Less than that of Jupiter

  2. More than that of Jupiter

  3. Equal to that of Jupiter or saturn

  4. More than that of saturn.

Show answer
Correct Option: A
Explanation:

We don't know the exact order of all the planets, but Jupiter formed first, with Saturn close behind. Both were finished in less than 3 million years. The inner planets (Mercury, Venus, Earth, Mars) got off to a late start.

We don't observe space contraction in our every day lives and the reason is
lorentz transformation and muon experiment option a: relativity physics

  1. Space contraction is not noticeable until objects approach the speed of light.

  2. Space contraction does not occur until objects approach the speed of light.

  3. Space contraction only occurs in a vacuum.

  4. Space contraction is offset by the effect of gravity.

  5. Acceleration is necessary for length contraction.

Show answer
Correct Option: A
Explanation:

The contracted length of objects moving relative to an observer with speed $v$ is given by $l'=l _0\sqrt{1-(\dfrac{v}{c})^2}$.

Hence at small speeds $v<<c$, $l'\approx l _0$, and hence the space contraction is not noticeable.

The best definition for space contraction ?
lorentz transformation and muon experiment option a: relativity physics

  1. The length of an object decreases in the same direction it is moving.

  2. All dimensions of an object decrease at high speeds.

  3. The length of an object increases in the same direction it is moving.

  4. Both length and width, but not depth, decrease at high speeds.

  5. Space is constant regardless of its location or state of motion.

Show answer
Correct Option: A
Explanation:

When an object is moving relative to an observer, the length of the object as observed by a moving observer is less than that observed by a stationary one in the direction of the movement.

A rod of rest length L moves at a relativistic speed. Let L' = L/$\gamma$. Its length

lorentz transformation and muon experiment option a: relativity physics

  1. must be equal to L'

  2. may be equal to L

  3. may be more than L' but less than L

  4. may be more than L

Show answer
Correct Option: B,C

A man is sitting inside a moving train and observes the objects outside of the train. Then choose the single correct choice from the following statements

lorentz transformation and muon experiment option a: relativity physics

  1. all stationary objects outside the train will move with same velocity in opposite direction of the train with respect to the man.

  2. Stationary objects near the train will move with grater velocity & object far from train will move with lesser velocity with respect to the man

  3. large objects like moon or mountains will move with same velocity as that of the train

  4. all of these.

Show answer
Correct Option: A
Explanation:

All small objects will move in opposite direction of train with same velocity.

Far objects like moon will appear stationary.

According to special relativity, which of the following people would see me aging most slowly? (I am sitting)

lorentz transformation and muon experiment option a: relativity physics

  1. A person running by me at $6.0\ m/s$

  2. A person sitting next to me in a rocket travelling at half the speed of light

  3. A person viewing me from the top of a mountain

  4. A person beside me on a bus moving at $15 m/s$

  5. All people would see me age at the same rate

Show answer
Correct Option: B
Explanation:
A person sitting next to me in a rocket travelling at half the speed of light will see the person ageing more slowly, as faster an object is accelerated to, the higher the degree of time dilation effect relative to an object of lower speed.
Einstein's theory of relativity works on a human scale: the higher you are, the faster you age.

A person is watching a rocket with an astronaut inside move by at a speed near the speed of light.
Which of the following statement is true?

lorentz transformation and muon experiment option a: relativity physics

  1. The passage of time on the astronaut's watch is faster from the person's perspective than from the astronaut's

  2. The passage of time on the astronaut's watch is the same from the perspective of the person and the astronaut

  3. The passage of time on the astronaut's watch is faster from the perspective of the astronaut than from the perspective of the person

  4. The passage of time on the person's watch is faster, from his own perspective, as the rocket files by, than it was before the rocket flew by

  5. The passage of time on the astronaut's watch is faster, from his own perspective, as he flies by the person, than it was before he flew by the person

Show answer
Correct Option: A
Explanation:

Passage of time as measured by the person in rest frame           $t = \dfrac{\tau}{\sqrt{1-v^2/c^2}}$      $\implies t>\tau$

where  $\tau$ is the passage of time as measured by the astronaut in moving frame. 
$\implies$ Watch in a moving frame runs at a slower rate than that in rest frame.
Thus passage of time on the astronaut's watch is faster from the person's perspective than from the astronaut's perspective. 

The length of cruiser is $200 m$. If If the cruiser travels at a speed of $(\dfrac{\sqrt{3}}{2})c$ past a planet. Calculate the length of the cruiser measured by the inhabitants of the planet.

lorentz transformation and muon experiment option a: relativity physics

  1. $0$

  2. Between $0$ and $200 m$

  3. $200 m$

  4. Greater than $200 m$

  5. None of the above, since it is impossible to reach the described speed

Show answer
Correct Option: B
Explanation:

According to the theory of relativity, the length of objects observed by a moving frame is less as compared to that observed by the rest frame. This is called length contraction.

The planet for the cruiser is a moving frame, and the cruiser itself is rest frame for it. Thus the length of cruiser as observed by observer on planet is less than $200m$.