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If the length of a simple pendulum is doubled keeping its amplitude constant its energy will bea)Unchangedb)Doubledc)Four timesd)Halved

Ranjeet Gupta , 5 Years ago
Grade 12
anser 3 Answers
Arun

Last Activity: 5 Years ago

 

As we learnt in

Time period of oscillation of simple pendulum -

T=2\pi \sqrt{\frac{l}{g}}

- wherein

l = length of pendulum 

g = acceleration due to gravity.

 

 Halved

 

Hence option D is correct

Sanjeev Narang

Last Activity: 5 Years ago

Simple pendulum is doing simple harmonic motion . so, Total energy is given by:
      T. E. = 1/2*m*A2*(\omega)2 
But (\omega)2 =g/l
Then, T. E. =1/2*m*A2*g/l
As mass(m), 1/2, Amplitude(A), and Acceleration due to gravity(g) are constant, then:
         T. E. is inversely proportional to length of the simple pendulum(l). Therefore if length become doubled T.E. becomes halved.
So option (d) is the answer. 
 
 

Khimraj

Last Activity: 5 Years ago

 
the answer is (d) halved. we know the formula t = 2pi * root(l/g).
so when l’ = 2l. t becomes root(2) times more. 

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