Two simple pendulums whose lengths are 100 cm and 121 cm are susp… - Vidyadip

MCQ

Two simple pendulums whose lengths are $100 cm$ and $121 cm$ are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will the two be in phase again

A
$11$
✓
$10$
C
$21$
D
$20$

✓

Answer

Correct option: B.

$10$

b
(b) Let ${T_1}$ and ${T_2}$ are the time period of the two pendulums ${T_1} = 2\pi \sqrt {\frac{{100}}{g}} $ and ${T_2} = 2\pi \sqrt {\frac{{121}}{g}} $
$({T_1} < {T_2}$ because ${l_1} < {l_2})$.
Let at $t = 0$, they start swinging together. Since their time periods are different, the swinging will not be in unision always.

Only when number of completed oscillation differs by an integer, the two pendulum will again begin to swing together.

Let longer length pendulum complete $n$ oscillation and shorter length pendulum complete $(n+1)$ oscillation, for the unision swinging, then $(n + 1){T_1} = n{T_2}$
$(n + 1) \times 2\pi \sqrt {\frac{{100}}{g}} = n \times 2\pi \sqrt {\frac{{121}}{g}} $$ \Rightarrow n = 10$

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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A body of mass $5 \times 10^{3} \,kg$ moving with speed $2\, m / s$ collides with a body of mass $15 \times 10^{3} \,kg$ in elastically and sticks to it. Then loss in $K. E.$ of the system will be (in $KJ$)

The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is

The relative error in the determination of the surface area of a sphere is $\alpha $. Then the relative error in the determination of its volume is

What will be the acceleration of the system and tension in the rope connecting $5\,kg$ and $1\,kg$ :-

A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will be

In some region, the gravitational field is zero. The gravitational potential in this region

A gas at $27^o C$ has a volume $V$ and pressure $P.$ On heating its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be ...... $^oC$

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

$(A)$For a given material of the capillary tube, $\mathrm{h}$ decreases with increase in $\mathrm{r}$.

$(B)$ For a given material of the capillary tube, $\mathrm{h}$ is independent of $\sigma$

$(C)$ If this experiment is performed in a lift going up with a constant acceleration, then $\mathrm{h}$ decreases

$(D)$ $\mathrm{h}$ is proportional to contact angel $\theta$

A metal ball immersed in alcohol weighs ${W_1}$ at $0°C$ and ${W_2}$ at $59°C.$ The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of metal is large compared to that of alcohol, it can be shown that

The latent heat of vaporization of a substance is always