Two springs of force constant K and 2K are connected to a mass as… - Vidyadip

MCQ

Two springs of force constant $K$ and $2K$ are connected to a mass as shown below. The frequency of oscillation of the mass is

A
$\frac{{3K}}{M}$
B
$\pi \,\sqrt {\frac{{6M}}{K}} $
C
$\frac{1}{{2\pi }}\,\sqrt {\frac{{3K}}{M}} $
✓
$\frac{1}{\pi }\,\sqrt {\frac{K}{{6M}}} $

✓

Answer

Correct option: D.

$\frac{1}{\pi }\,\sqrt {\frac{K}{{6M}}} $

d
$\frac{1}{\mathrm{K}_{\mathrm{eq}}}=\frac{1}{\mathrm{K}_{1}}+\frac{1}{\mathrm{K}_{2}}$

$=\frac{1}{\mathrm{K}}+\frac{1}{2 \mathrm{K}}$

$\mathrm{Keq}=\frac{2 \mathrm{K}}{3}$

$\mathrm{n}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{K} / 3}{\mathrm{M}}}=\frac{1}{\pi} \sqrt{\frac{\mathrm{K}}{6 \mathrm{M}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 13. oscillations→13. oscillations — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

What is the velocity of a statellite intersecting in a parking orbit ?

In the expression for time period $T$ of simple pendulum $T=2 \pi \sqrt{\frac{l}{g}}$, if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively then percentage error in acceleration due to gravity $g$ is equal to ......... $\%$

The change in potential energy when a body of mass $m$ is raised to height $n R$ from the earth's surface is ( $R$ is radius of earth)

A body of mass $m$ collides against a wall with the velocity $v$ and rebounds with the same speed. Its change of momentum is:

A wheel of radius 20cm is pushed to move it on a rough horizontal surface. It is found to move through a distance of 60cm on they road during the time it completes one revolution about the centre. Assume that the linear and the angular accelerations are uniform. The frictional force acting on the wheel by the surface is:

The graph of position $x$ versus time $t$ represents the motion of a particle. If $b$ and $c$ are both positive constants, which of the following expressions best describes the acceleration $a$ of the particle?

A rocket with a lift-off mass $2 \times 10^4\,kg$ is blasted upwards with an intial acceleration of $5\,m\,s^{-2}$ . The initial thrust of the blast is (Take $g = 10\,m\,s^{-2}$ )

A light balloon filled with helium of density $\rho_{ He }$ is tied to a long light string of length $l$ and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released. Then,

The separation between the plates of a charged parallel$-$plate capacitor is increased. Which of the following quantities will change?

Charge on the capacitor.
Potential difference across the capacitor.
Energy of the capacitor.
Energy density between the plates.

In the ideal gas equation PV = nRT the value of R depends on: