The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$, is given by
IIT 2000,JEE MAIN 2022, Medium
Download our app for free and get started
(a) See the following force diagram. Vehicle is moving down the frictionless inclined surface so, it's acceleration is $g\sin \theta $. Since vehicle is accelerating, a pseudo force $m(g\sin \theta )$ will act on bob of pendulum which cancel the $\sin \theta $ component of weight of the bob.
Hence net force on the bob is $F_{net} = mg\cos \theta $ or net acceleration of the bob is ${g_{eff}} = g\cos \theta $
$\therefore $ Time period $T = 2\pi \sqrt {\frac{l}{{{g_{eff}}}}} = 2\pi \sqrt {\frac{l}{{g\cos \theta }}} $
Download our appand 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
- 1On a planet a freely falling body takes $2 \,sec$ when it is dropped from a height of $8 \,m$, the time period of simple pendulum of length $1\, m$ on that planet is ..... $\sec$View Solution
- 2View SolutionWhich of the following statements is not true ? In the case of a simple pendulum for small amplitudes the period of oscillation is
- 3A simple pendulum has time period $T$. The bob is given negative charge and surface below it is given positive charge. The new time period will beView Solution
- 4$Assertion :$ The time-period of pendulum, on a satellite orbiting the earth is infinity.View Solution
$Reason :$ Time-period of a pendulum is inversely proportional to $\sqrt g$ - 5A particle is excuting a simple harmonic motion. Its maximum acceleration is $\alpha $ and maximum velocity is $\beta $. Then its frequency of vibration will beView Solution
- 6A spring of force constant $k$ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant ofView Solution
- 7View SolutionA tunnel has been dug through the centre of the earth and a ball is released in it. It will reach the other end of the tunnel after
- 8The equation of $S.H.M.$ is $y = a\sin (2\pi nt + \alpha )$, then its phase at time $t$ isView Solution
- 9For a particle executing $S.H.M.,\, x =$ displacement from equilibrium position, $v =$ velocity at any instant and $a =$ acceleration at any instant, thenView Solution
- 10A simple harmonic motion having an amplitude $A$ and time period $T$ is represented by the equation : $y = 5 \sin \pi (t + 4) m$View Solution
Then the values of $A$ (in $m$) and $T$ (in $sec$) are :