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Question: A uniform spring of force constant k is cut into two pieces, the lengths of which are in the ratio 1...

A uniform spring of force constant k is cut into two pieces, the lengths of which are in the ratio 1 : 2. The ratio of the force constants of the shorter and the longer pieces is

A

1 : 3

B

1 : 2

C

2 : 3

D

2 : 1

Answer

2 : 1

Explanation

Solution

Force constant (k)∝1 Length of the spring (l)( k ) \propto \frac { 1 } { \text { Length of the spring } ( l ) }

⇒ k1k2=l2l1=21\frac { k _ { 1 } } { k _ { 2 } } = \frac { l _ { 2 } } { l _ { 1 } } = \frac { 2 } { 1 }