A pendulum suspended from ceiling of a train has a period T when train is at rest. When train travel

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13.Oscillations

easy

A pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels same distance per unit time, the period of oscillation is

Increase

Remains unaffected

Become twice

Decrease

Solution

When a train is moving with acceleration, the pendulum is exerted by a pseudo acceleration opposite to the direction of the train. As a result, there will be an increase in effective acceleration on the pendulum. The time period will decrease as the time period is inversely proportional to the square root of effective acceleration.

Standard 11

Physics

A simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration, the frequency of the simple pendulum will

easy

A clock which keeps correct time at ${20^o}C$, is subjected to ${40^o}C$. If coefficient of linear expansion of the pendulum is $12 \times {10^{ – 6}}/^\circ C$. How much will it gain or loose in time

hard

The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )

medium

(JEE MAIN-2022)

A simple pendulum with length $100\,cm$ and bob of mass $250\,g$ is executing S.H.M. of amplitude $10\,cm$. The maximum tension in the string is found to be $\frac{x}{40}\,N$. The value of $x$ is $……….$.

hard

(JEE MAIN-2023)

In the following table relation of graph in column$-I$ and shape of graph in column$-II$ is shown match them appropriately.

column$-I$ column $-II$

$(a)$ ${T^2} \to l$ $(i)$ Linear

$(b)$ ${T^2} \to g$ $(ii)$ Parabolic

$(c)$ ${T} \to l$ $(iii)$ Hyperbolic