An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a 10 μ F capacitor at a potential difference of 10000 V will be

Question

An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a 10 μ F capacitor at a potential difference of 10000 V will be (A) 1/4 (B) 1 (C) 1/2 (D) 2

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b3941d4624f57b51f89fb5f7dac9498d-.png" /> When a force of F newton is applied the potential energy is given by U=(1/2) F x Energy stored by capacitor is (1/2) C V2 . ∴ Ratio is ((1/2) F x/(1)2 C V2) =(5000 × 0.2/10 × 10-6(104)2)=1

Q. An automobile spring extends $0.2 m$ for $5000 N$ load. The ratio of potential energy stored in this spring when it has been compressed by $0.2 m$ to the potential energy stored in a $10 μ F$ capacitor at a potential difference of $10000 V$ will be

1/4

1

1/2

2

When a force of $F$ newton is applied the potential energy is given by
$U = \frac{1}{2} F x$
Energy stored by capacitor is $\frac{1}{2} C V^{2} .$
$∴$ Ratio is $\frac{\frac{1}{2} F x}{\frac{1}{2} C V ^{2}}$
$= \frac{5000 \times 0.2}{10 \times 1 0 ^{- 6} ( 1 0 ^{4} ) ^{2}} = 1$

Q. An automobile spring extends 0.2m for 5000N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2m to the potential energy stored in a 10μF capacitor at a potential difference of 10000V will be

1/4

1

1/2

2

When a force of F newton is applied the potential energy is given by U=21​Fx Energy stored by capacitor is 21​CV2. ∴Ratio is 21​CV221​Fx​ =10×10−6(104)25000×0.2​=1

Q. An automobile spring extends $0.2 m$ for $5000 N$ load. The ratio of potential energy stored in this spring when it has been compressed by $0.2 m$ to the potential energy stored in a $10 μ F$ capacitor at a potential difference of $10000 V$ will be

When a force of $F$ newton is applied the potential energy is given by
$U = \frac{1}{2} F x$
Energy stored by capacitor is $\frac{1}{2} C V^{2} .$
$∴$ Ratio is $\frac{\frac{1}{2} F x}{\frac{1}{2} C V ^{2}}$
$= \frac{5000 \times 0.2}{10 \times 1 0 ^{- 6} ( 1 0 ^{4} ) ^{2}} = 1$