A) 0.2 N
B) 0.3 N
C) 0.4 N
D) 0.6 N
Correct Answer: D
Solution :
Let extention produced in a spring of force constant k is\[x,\]then \[F=kx\] Given, \[F=0.1\text{ }N,\text{ }x=1.5\text{ }cm=1.5\times {{10}^{-2}}m\] \[\therefore \] \[k=\frac{F}{x}=\frac{0.1}{1.5\times {{10}^{-2}}}\] ?.(i) When the spring in cut into there equal parts, then spring constant of each part will be 3k. Now, force required \[F=3k(x)=3k(3\times {{10}^{-2}})\] Putting the value of k from Eq. (i), we get \[F=\frac{3\times 0.1}{(1.5\times {{10}^{-2}})}\times 3\times {{10}^{-2}}=0.6\,N\]
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