Question

A pendulum is executing simple harmonic motion and its maximum kinetic energy is K₁. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K₂ then:
(A) K₂ = 2K₁ (B) K₂
= K₁/2
(C) K₂
= K₁/4
(D) K₂ = K₁

Answer 1

Explanation:

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Answer 2

Answer:

Maximum kinetic energy =1/2mω  

2

A  

2

 

ω=  

L

g

​  

 

​  

 

A=Lθ

KE=1/2m  

L

g

​  

×L  

2

θ  

2

,     KE =1/2mgLθ  

2

 

K  

1

​  

=1/2mgLθ  

2

 

If length is doubled

K  

2

​  

=1/2mg(2L)θ  

2

 

K  

2

​  

 

K  

1

​  

 

​  

=  

1/2mg(2L)θ  

2

 

1/2mglθ  

2

 

​  

=  

2

1

​  

 

K  

2

​  

=2K  

1

​