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 10 microF capacitor at a potential difference of 10000 v Will be
1-1/4
2-1
3-1/2
4-2
For spring F=1/2kx2 and potential energy U=1/2Fx=0.5*0.2*5000=500J For capacitor potential energy U'=1/2CV2=0.5*10*[10]-6*10000*10000=500J. Therefore ratio of potential energy is 1:1
To find the ratio of potential energy stored in the automobile spring to the potential energy stored in the capacitor, we need to calculate the potential energy for both and then divide one by the other.
1. Potential Energy in the Automobile Spring:
The potential energy stored in a spring can be calculated using the formula:
Potential Energy = (1/2) * k * x^2
Where k is the spring constant and x is the displacement of the spring.
Given that the automobile spring extends by 0.2 m for a load of 5000 N, we have the displacement (x) as 0.2 m.
To calculate the spring constant (k), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement:
Force = k * x
Rearranging the formula, we get:
k = Force / x
Substituting the values, we have:
k = 5000 N / 0.2 m = 25000 N/m
Now, we can calculate the potential energy in the spring using the formula:
Potential Energy in Spring = (1/2) * k * x^2
Potential Energy in Spring = (1/2) * 25000 N/m * (0.2 m)^2
Potential Energy in Spring = 500 N
2. Potential Energy in the Capacitor:
The potential energy stored in a capacitor can be calculated using the formula:
Potential Energy = (1/2) * C * V^2
Where C is the capacitance and V is the potential difference.
Given that the capacitance (C) is 10 microF (which is equivalent to 10 * 10^-6 F) and the potential difference (V) is 10000 V, we can calculate the potential energy in the capacitor using the formula:
Potential Energy in Capacitor = (1/2) * C * V^2
Potential Energy in Capacitor = (1/2) * 10 * 10^-6 F * (10000 V)^2
Potential Energy in Capacitor = 0.05 J (or 50 mJ)
3. Ratio of Potential Energies:
Now, let's calculate the ratio of the potential energy stored in the spring to the potential energy stored in the capacitor:
Ratio = (Potential Energy in Spring) / (Potential Energy in Capacitor)
Ratio = 500 N / 0.05 J
Ratio = 10000
So, the ratio of potential energy stored in the automobile spring when it has been compressed by 0.2 m to the potential energy stored in the 10 microF capacitor at a potential difference of 10000 V is 10000.
Therefore, the answer is not provided in the options given (1-1/4, 2-1, 3-1/2, 4-2).