Tag: option b: engineering physics

Questions Related to option b: engineering physics

In damped oscillation mass is $1\ kg$ and spring constant $=100\ N/m$, damping coefficeint$=0.5\ kg\ s^{-1}$. If the mass displaced by $10\ cm$ from its mean position then what will be the value of its mechanical energy after $4$ seconds?

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. $0.67\ J$

  2. $0.067\ J$

  3. $6.7\ J$

  4. $0.5\ J$

Show answer
Correct Option: B
Explanation:
Given,

Mass, $m=1\,kg$

Spring constant, $k=100\,N/m^2$

Damping coefficient, $b=0.5\,kg/s$

Distance, $x=10\,cm$

Time, $t=4\,s$

We know,

The energy for damped oscillation, $E=\dfrac 12kx^2 e^{-\dfrac{bt}{m}}$

$E=\dfrac 12\times 100\times 0.01\times e^{-\dfrac{0.5\times 4}{1}}$

$E=\dfrac{e^{-2}}{2}=0.067\,J$

Hence the mechanical energy is $0.067\,J$

In reality, a spring won't oscillate for ever.               will                the amplitude of oscillation until eventually the system is at rest.

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. Frictional force, increase

  2. Viscous force, decrease

  3. Frictional force, decrease

  4. Viscous force, increase

Show answer
Correct Option: C
Explanation:

In reality, a spring won't oscillate forever. Frictional force will decrease the oscillation until eventually, the system is at rest.

Undamped oscillations are practically impossible because

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. there is always loss of energy.

  2. there is no force opposing friction.

  3. energy is not conserved in such oscillations.

  4. None of these.

Show answer
Correct Option: A
Explanation:

Underdamped oscillation is practical because there always be resistive force present in reality which will try to make an oscillating body to lose its energy. This loss of energy makes the motion damped motion.

Dampers are found on bridges

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. to allow natural oscillations to occur.

  2. to prevent them from swaying due to wind.

  3. to prevent resonance of frequencies.

  4. None of these.

Show answer
Correct Option: B
Explanation:

Dampers are found bridges to prevent them from swaying due to wind otherwise this motion can hamper the condition of a bridge.

If we wish to represent the equation for the position of the mass in terms of a differential equation, which one of these would be the most suitable?

physics option b: engineering physics introduction to sound free, forced and damped oscillations resonance

  1. $ m \dfrac{d^2x}{dt^2} + b \dfrac{dx}{dt} + kx = 0$

  2. $ m \dfrac{d^2x}{dt^2} - b \dfrac{dx}{dt} + kx = 0$

  3. $ m \dfrac{d^2x}{dt^2} + b \dfrac{dx}{dt} - kx = 0$

  4. $ m \dfrac{d^2x}{dt^2} -b \dfrac{dx}{dt} - kx = 0$

Show answer
Correct Option: A
Explanation:

The force on body oscillating in resistive medium is 

$f = -kx - bv$
$\Rightarrow m\dfrac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =-kx-b\dfrac { dx }{ dt } \ \Rightarrow m\dfrac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +b\dfrac { dx }{ dt } +kx=0$
k = oscillating constant 
x = displacement of body from mean position 
b = constant depends on resistive medium 
v = velocity of object = $\dfrac{dx}{dt}$
m = mass of object .

Buoyant force is directed

physics floatation buoyancy fluid pressure option b: engineering physics

  1. upwards

  2. downwards

  3. sideways

  4. at ll directions

Show answer
Correct Option: A
Explanation:

As evident from Archimedes' principle, buoyant force is the force applied upward on any object by a fluid.

When a solid is completely immersed in a fluid, the apparent loss of weight of solid is _______ volume of fluid displaced 

physics floatation buoyancy fluid pressure option b: engineering physics

  1. more than

  2. less than

  3. equal to

  4. cant say

Show answer
Correct Option: C
Explanation:

From the principle of Archimedes, loss of weight is equal to the weight of the liquid displaced.

When a body is fully immersed in a liquid the apparent loss in the weight of body is equal to :

physics floatation buoyancy fluid pressure option b: engineering physics

  1. volume of liquid displaced by the body

  2. density of the liquid

  3. weight of liquid displaced by the body

  4. none of these

Show answer
Correct Option: C
Explanation:

According to Archimedes principle, the weight of water displaced is equal to the weight of immersed part.For a solid floating in a liquid, its weight acting vertically down at its centre of gravity is equal to the weight of the liquid displaced by the immersed part of the solid acting vertically up at its centre of buoyancy. In the floating condition, the apparent weight and the apparent density of the solid are zero and the body is said to be weightless.

State whether the weight of an iron sinker with cork combined in water will be more or less than that of the iron sinker alone in water. 

physics floatation buoyancy fluid pressure option b: engineering physics

  1. Less

  2. More

  3. Same

  4. None of the above

Show answer
Correct Option: A
Explanation:

The weight of an iron sinker with cork combined in water will be less than that of the iron sinker alone in water.
This is because upthrust on cork due to water (when completely immersed) is greater than its weight.

An incompressible liquid of density $\rho$ is contained in a vessel of uniform cross-sectional area $A$. If then atmospheric pressure is $p$, then the force acting on a horizontal plane of area a situated at a depth $d$ in liquid is given by

physics option b: engineering physics buoyancy floatation fluid pressure

  1. $Ap+apgd$

  2. $\dfrac { p }{ A } +\dfrac { \rho gd }{ a }$

  3. $\dfrac { p+\rho gd }{ a }$

  4. $a\left( \rho\ gd+p \right)$

Show answer
Correct Option: D