A uniform spring has an unstretched length L and a force constant k . The spring is cut into two parts of unstretched lengths l1 and l2 such that l2=η l2 , where η is an integer. The corresponding force constants are k1 and k2 , then

Question

A uniform spring has an unstretched length L and a force constant k . The spring is cut into two parts of unstretched lengths l1 and l2 such that l2=η l2 , where η is an integer. The corresponding force constants are k1 and k2 , then (A) force has to be kept same to find k1 and k2 (B) k1=(k (η + 1)/η) and k2=k(η - 1) (C) k1=(k (η - 1)/η) and k2=k(η + 1) (D) k1=(k (η + 1)/η) and k2=k(η + 1)

Tardigrade Admin · Accepted Answer

In case of cutting of a spring, l× k=constant k1l1=k2l2 k1(η l2)=k2l2 ⇒ η k1=k2 ...............(1) Now both the springs when connected in series should give the same effect as that of the original spring. Hence, by applying the concept of springs connected in series, we obtain, (1/k)=(1/k1)+(1/k2) ...............(2) (1/k)=(1/k1)+(1/η k1) ⇒ (k1/k)=(η + 1/η) (using (1)) k1=((η + 1/η))k ............(3) Using (3) again in (2), we obtain, k2=(η + 1)k

Q. A uniform spring has an unstretched length $L$ and a force constant $k$ . The spring is cut into two parts of unstretched lengths $l_{1}$ and $l_{2}$ such that $l_{2} = η l_{2}$ , where $η$ is an integer. The corresponding force constants are $k_{1}$ and $k_{2}$ , then

force has to be kept same to find $k_{1}$ and $k_{2}$

$k_{1} = \frac{k ( η + 1 )}{η}$ and $k_{2} = k (η - 1)$

$k_{1} = \frac{k ( η - 1 )}{η}$ and $k_{2} = k (η + 1)$

$k_{1} = \frac{k ( η + 1 )}{η}$ and $k_{2} = k (η + 1)$

Q. A uniform spring has an unstretched length L and a force constant k . The spring is cut into two parts of unstretched lengths l1​ and l2​ such that l2​=ηl2​ , where η is an integer. The corresponding force constants are k1​ and k2​ , then

force has to be kept same to find k1​ and k2​

k1​=ηk(η+1)​ and k2​=k(η−1)

k1​=ηk(η−1)​ and k2​=k(η+1)

k1​=ηk(η+1)​ and k2​=k(η+1)

Q. A uniform spring has an unstretched length $L$ and a force constant $k$ . The spring is cut into two parts of unstretched lengths $l_{1}$ and $l_{2}$ such that $l_{2} = η l_{2}$ , where $η$ is an integer. The corresponding force constants are $k_{1}$ and $k_{2}$ , then

force has to be kept same to find $k_{1}$ and $k_{2}$

$k_{1} = \frac{k ( η + 1 )}{η}$ and $k_{2} = k (η - 1)$

$k_{1} = \frac{k ( η - 1 )}{η}$ and $k_{2} = k (η + 1)$

$k_{1} = \frac{k ( η + 1 )}{η}$ and $k_{2} = k (η + 1)$