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A mass m can rotate with angular velocity w1 on a smooth horizontal table being attached to a spring whose other end having passes through a hole in the table, supports another mass m.This other mass turns around as a conical pendulum with angular velocity w2. if l1 and l2 are the lengths of the string on and below table then a)l1:l2=w1^2:w2^2 b)l1:l2=w2^2:w1^2 c)l1:l2=w1:w2 d0 none

A mass m can rotate with angular velocity w1 on a smooth horizontal table being attached to a spring whose other end having passes through a hole in the table, supports another mass m.This other mass turns around as a conical pendulum with angular velocity w2. if l1 and l2 are the lengths of the string on and below table then


a)l1:l2=w1^2:w2^2


b)l1:l2=w2^2:w1^2


c)l1:l2=w1:w2


d0 none

Grade:11

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Kritika,

 

Let "x" be the elongation in the spring.

 

So for the mass above the table

Kx = ml1w12

 

And for the mass below the table, let "Q" be the angle made by the spring with the vertical.

So kxsinQ = mrw22.

From the right triangle l2sinQ = r

So kxsinQ = m(l2sinQ)w22.

 

Hence l1:l2 = w22:w12.

 

Optoin (B)

 

Hope that helps.

 

Best Regards,

Ashwin (IIT Madras).

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