Tag: motion of a mass suspended by two springs

Quizzes (0) Questions (47)

Questions Related to motion of a mass suspended by two springs

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 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)