Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7:8, then the ratio of lengths of the two pendulums will be

Question

Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7:8, then the ratio of lengths of the two pendulums will be (A)  7:8  (B)  8:7  (C)  49:64  (D)  64:49

Tardigrade Admin · Accepted Answer

Suppose at t =0, pendulums beings to given ro swing simultaneously. Hence they will again swing simultaneously if n 1 T 1= n 2 T 2 ⇒ ( n 1/ n 2)=( T 2/ T 1)=√( l 2/ l 1) ⇒ ( l 1/ l 2)=(( n 2/ n 1))2 =((8/7))2=(64/49)

Q. Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7 : 8,$ then the ratio of lengths of the two pendulums will be

$7 : 8$

$8 : 7$

$49 : 64$

$64 : 49$

Q. Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7:8, then the ratio of lengths of the two pendulums will be

7:8

8:7

49:64

64:49

Suppose at t=0, pendulums beings to given ro​ swing simultaneously. Hence they will again swing simultaneously if n1​T1​=n2​T2​ ⇒n2​n1​​=T1​T2​​=l1​l2​​​ ⇒l2​l1​​=(n1​n2​​)2 =(78​)2=4964​

Q. Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7 : 8,$ then the ratio of lengths of the two pendulums will be

$7 : 8$

$8 : 7$

$49 : 64$

$64 : 49$