Simple pendulum
- If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x/2 times its original time period. Then the value of x is: Answer: 3. sqrt2 Key idea: T=2π√(L/g) does not depend on the mass of the bob. Only the length changes: T'=2π√(L/2/g)=T/sqrt2 . Setting T/sqr... 1
- Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean pos… Answer: 2. 11 Time period T∝sqrt l , so T₁₂₁:T₁₀₀=11:10 . They are next in phase when the shorter pendulum has made one more vibration than... 1
- A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s^2 at a distance of 5 m from the mean position. The time period o… Answer: 3. π s For SHM, a=ω²x . ω²=20/5=4⇒ω=2\ mathrmrad s⁻¹ . T=2π/ω=π\ s 1