A spring of force constant k is cut into two parts such that length of one part is double to another part. What will be the force constant of larger part?

Options

A. `(2)/(3)k`
B. `(3)/(2)k`
C. `3k`
D. `6k`

Answer

B

Explanation

Force constant of spring is inversely proportional to its length,
`therefore k propto (1)/(l)`
`therefore kl = 1" ""…….."(1)`
Given that `l_(1)= 2l_(2)`
and `l= l_(1)+l_(2)`
`=2l_(2)+l_(2)`
`l= 3l_(2)`
and `l= l_(1)+(l_1)/(2)= (3l_1)/(2)" ""........."(2)`
Now, `k_(1)l_(1)= k_(2)l_(2) = kl`
`therefore k_(1)l_(1) = kl`
`k_(1)l_(1)= k xx (3l_1)/(2)` [From equation (1)]
`therefore k_(1)= (3)/(2)k`.