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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.

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

When two blocks connected by a spring move towards each other under mutual interaction:

  1. Their velocities are equal and opposite

  2. Their accelerations are equal and opposite

  3. The forces acting on them are equal and opposite

  4. Their momenta are equal and opposite.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If we take the two blocks plus spring as the system there is no external force acting on this system.
The accelerations will be equal and opposite if masses are equal. Since the forces are internal, they will be equal and opposite.

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

Two springs have their force constants ${ K } _ { 1 }$ and ${ K } _ { 2 }.$ Both are stretched till their elastic energies are equal. Then,ratio of stretching forces ${ K } _ { 1 } / { K } _ { 2 }$ is equal to:

  1. $K _ { 1 } / K _ { 2 }$
  2. $\mathbf { K } _ { 2 } : \mathbf { K } _ { 1 }$
  3. $\sqrt { K _ { 1 } } : \sqrt { K _ { 2 } }$
  4. $\mathbf { K } _ { 2 } ^ { 2 } : \mathbf { K } _ { 2 } ^ { 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Elastic energy U = F^2 / (2k). If U1 = U2, then F1^2 / (2k1) = F2^2 / (2k2). Rearranging gives (F1/F2)^2 = k1/k2, so F1/F2 = sqrt(k1)/sqrt(k2).

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

A mass of 2 kg falls from a height of 40 cm, on a spring with a force constant of 1960 N/m. The spring is compressed by ? (Take $g=9.8m/s^2$)

  1. 9 cm

  2. 1.0 cm

  3. 20 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using conservation of energy: m * g * (h + x) = 1/2 * k * x^2. Plugging in m=2, g=9.8, h=0.4, k=1960 results in a quadratic equation for compression x. Solving this yields x = 0.09m or 9cm.

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

One end of a light spring of force constant K is fixed to ceiling the other end is fixed to block of mass M initially the spring is relaxed the work done by the external agent to lower the Hanging body of mass M slowly till it comes to equilibrium is

  1. $3 m^2 g^2/ 2k$
  2. $m^2 g^2/ 2k$
  3. $-3 m^2 g^2/ 2k$
  4. $- m^2 g^2/ 2k$
Reveal answer Fill a bubble to check yourself
A Correct answer