If two similar springs each of spring constant $K _{1}$ are joined in series, the new spring constant and time period would be changed by a factor
  • A$\frac{1}{2}, \sqrt{2}$
  • B$\frac{1}{4}, \sqrt{2}$
  • C$\frac{1}{4}, 2 \sqrt{2}$
  • D$\frac{1}{2}, 2 \sqrt{2}$
JEE MAIN 2021, Medium
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from $10\, cm$ to $8\, cm$ in $40\, seconds$ . Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is $1.3$ . The time in which amplitude of this pendulum will reduce from $10\, cm$ to $5\, cm$ in carbon dioxide will be close to ..... $s$ $(ln\, 5 = 1.601,ln\, 2 = 0 .693)$
    View Solution
  • 2
    A particle is moving in a circle with uniform speed. Its motion is
    View Solution
  • 3
    A point object is kept in front of a plane mirror. The plane mirror is doing $SHM$ of amplitude $2\,cm$. The plane mirror moves along the $x-$ axis and $x-$ axis is normal to the mirror. The amplitude of the mirror is such that the object is always infront of the mirror. The amplitude of $SHM$ of the image is .... $cm$
    View Solution
  • 4
    If a simple pendulum oscillates with an amplitude of $50\, mm$ and time period of $2\, sec$, then its maximum velocity is .... $m/s$
    View Solution
  • 5
    A block with mass $M$ is connected by a massless spring with stiffiess constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: ($i$) when the block is at $x_0$; and ($ii$) when the block is at $x=x_0+A$. In both the cases, a perticle with mass $m$ is placed on the mass $M$ ?

    ($A$) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m+M}}$, whereas in the second case it remains unchanged

    ($B$) The final time period of oscillation in both the cases is same

    ($C$) The total energy decreases in both the cases

    ($D$) The instantaneous speed at $x_0$ of the combined masses decreases in both the cases

    View Solution
  • 6
    The vertical extension in a light spring by a weight of $1\, kg$ suspended from the wire is $9.8\, cm$. The period of oscillation
    View Solution
  • 7
    The acceleration due to gravity at a place is ${\pi ^2}\,m/se{c^2}$. Then the time period of a simple pendulum of length one metre is
    View Solution
  • 8
    A lift is descending with acceleration $g/3$ . What will be the time period of a simple pendulum suspended from its ceiling if its time period in staionary life is $'T'$ ?
    View Solution
  • 9
    Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures

    $x\left( t \right) = A\,\sin \,\left( {at + \delta } \right)$

    $y\left( t \right) = B\,\sin \,\left( {bt} \right)$

    Identify the correct match below

    View Solution
  • 10
    The potential energy of a particle of mass $1\, kg$ in motion along the $x-$ axis is given by $U = 4\,(1 -cos\,2x)$, where $x$ is in $metres$ . The period of small oscillation (in $second$ ) is
    View Solution