Tag: oscillatory motion

Quizzes (7) Questions (124)

Questions Related to oscillatory motion

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

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

  1. $3k$
  2. $\dfrac{k}{3}$
  3. $k$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The spring constant k is inversely proportional to the length of the spring (k * L = constant). If a spring is cut into 3 equal parts, each part has a length of L/3, so its spring constant becomes 3k.

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

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 .......... 

  1. 2mg/k, mg/k

  2. mg/k, mg/k

  3. mg/k, 2mg/k

  4. 2mg/k, 2mg/k
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a mass is released suddenly, the maximum compression is 2mg/k due to energy conservation (potential energy lost equals elastic potential energy gained). At equilibrium, the forces balance (mg = kx), resulting in a compression of mg/k.

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

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 $10gm$.

  1. $10gm$
  2. $0gm$
  3. $1gm$
  4. $None$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When an elevator falls freely, it is in a state of weightlessness (acceleration equals acceleration due to gravity downwards). Any object inside experiences an effective acceleration of zero, so the spring balance reads 0 gm.

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

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?

  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. $\dfrac { 2 m v ^ { 2 } } { x ^ { 2 } }$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
$\begin{array}{l} \left( { \dfrac { 1 }{ 2 }  } \right) m{ v^{ 2 } }=\dfrac { 1 }{ 2 } m{ \left( { \dfrac { v }{ 2 }  } \right) ^{ 2 } }+\dfrac { 1 }{ 2 } k{ v^{ 2 } } \ \dfrac { 1 }{ 2 } k{ v^{ 2 } }=\dfrac { 1 }{ 2 } m{ \left( { \dfrac { v }{ 2 }  } \right) ^{ 2 } }-\dfrac { 1 }{ 2 } \left( { m{ v^{ 2 } } } \right)  \ k{ x^{ 2 } }=m\left( { { v^{ 2 } }-\dfrac { { { v^{ 2 } } } }{ 4 }  } \right)  \ k{ x^{ 2 } }=\dfrac { { 3m{ v^{ ^{ 2 } } } } }{ 4 }  \ \therefore k=\dfrac { { 3m{ v^{ ^{ 2 } } } } }{ { 4{ x^{ 2 } } } }  \end{array}$

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

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

  1. $5\ grams$
  2. $10\ grams$
  3. $20\ grams$
  4. $40\ grams$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $

 

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

Will it make any difference in the extension of the spring, if 3 springs of spring constant k are joined in series to life a load W as compared to one string of spring constant k to lift the same load

  1. Extension in long spring < extension in shorter spring

  2. Extension in long spring > extension in shorter spring

  3. Extension in both the springs are same

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If three springs are joined together, their effective spring constant will be k/3. Since load is W, we can write $W=(k/3)x _1$.

If these strings are replaced by a long spring of spring constant k, let the extension of the load be W, we can still write $W=kx _2$

Comparing these two equations, we get, $x _2=x _1/3$ or the extension in the long spring is less than the shorter springs

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

If two springs of spring constants $k _1$ and $k _2$ whose extensions upon applying a force F are $x _1$ and $x _2$ respectively are joined together in a series configuration, the net extension will be 

  1. $x= F(1/k _1+1/k _2)$
  2. $x= F(1/k _1-1/k _2)$
  3. $x= F(k _1+k _2)$
  4. $x= F(k _1-k _2)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x _1 = F/k _1$ and $x _2=F/k _2$

Upon joining both the springs together, the net extension will be $x =x _1+x _2$

Substituting, we get, $x= F(1/k _1+1/k _2)$

The correct option is (a)


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

A spring of force constant k is cut into 4 equal parts. The spring constant of each piece become_______ times and time period will become______ times.

  1. [5, 1/2]

  2. [4, 1/2]

  3. [7, 1/2]

  4. [4, 1/3]
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cutting a spring into 4 equal parts makes the spring constant of each piece 4k. The time period T = 2 * pi * sqrt(m/k). Since k becomes 4k, the new time period T' = 2 * pi * sqrt(m/4k) = T/2.