The length of a rubber cord is l1 metre when the tension is 4 N and l2 metre when the tension is 6 N . The length when the tension is 9 N, is

Question

The length of a rubber cord is l1 metre when the tension is 4 N and l2 metre when the tension is 6 N . The length when the tension is 9 N, is (A)  (2.5l2-1.5l1)m  (B)  (6l2-1.5l1)m  (C)  (3l2-2l1)m  (D)  (3.5l2-2.5l1)m

Tardigrade Admin · Accepted Answer

Let the original unstretched length be l. Y=(Stress/Strain)=(T/A/Δ l/l)=(T/A)× (l/Δ l) Now Y=(4/A)(l/(l1-l))=(6/A)(l/(l2-l)) =(9/A)(l/(l3-l)) ∴ 4(l3-l)=9(l1-l) ⇒ 4l3+5l=9l1 .... (i) Again, 6(l3-l)=9(l2-l) ⇒ 2l3+l=3l2 ...(ii) Solve Eqs. (i) and (ii), we obtain l3=(2.5l2-1.5l1)

Q. The length of a rubber cord is $l_{1}$ metre when the tension is $4 N$ and $l_{2}$ metre when the tension is $6 N$ . The length when the tension is $9 N$ , is

$(2.5 l_{2} - 1.5 l_{1}) m$

$(6 l_{2} - 1.5 l_{1}) m$

$(3 l_{2} - 2 l_{1}) m$

$(3.5 l_{2} - 2.5 l_{1}) m$

$(2.5 l_{2} + 1.5 l_{1}) m$

Q. The length of a rubber cord is l1​ metre when the tension is 4N and l2​ metre when the tension is 6N . The length when the tension is 9N, is

(2.5l2​−1.5l1​)m

(6l2​−1.5l1​)m

(3l2​−2l1​)m

(3.5l2​−2.5l1​)m