The potential energy of a spring increases by 15 J when stretched by 3 cm. If it is stretched by 4 cm, the increase in potential energy is

Question

The potential energy of a spring increases by 15 J when stretched by 3 cm. If it is stretched by 4 cm, the increase in potential energy is (A) 27 J (B) 30 J (C) 33 J (D) 36 J

Tardigrade Admin · Accepted Answer

Potential energy of spring, PE =(1/2) k x2 ⇒ PE propto x2 ∵ (( PE )2/( PE )1)=((x2/x1))2 ⇒ ( PE )2=( PE )1 ×((x2/x1))2 =15 ×((4/3))2=27 J

Q. The potential energy of a spring increases by $15 J$ when stretched by $3 c m$ . If it is stretched by $4 c m$ , the increase in potential energy is

27 J

30 J

33 J

36 J

Potential energy of spring, $PE = \frac{1}{2} k x^{2}$
$\Rightarrow PE \propto x^{2}$
$∵ \frac{( PE ) _{2}}{( PE ) _{1}} = (\frac{x _{2}}{x _{1}})^{2}$
$\Rightarrow (PE)_{2} = (PE)_{1} \times (\frac{x _{2}}{x _{1}})^{2}$
$= 15 \times (\frac{4}{3})^{2} = 27 J$

Q. The potential energy of a spring increases by 15J when stretched by 3cm. If it is stretched by 4cm, the increase in potential energy is