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A spring with spring constant k when stretched through 1 cm has a potential energy U. If it is stretched by 4 cm, the potential energy will become
  • a)
    4U
  • b)
    16U
  • c)
    8U
  • d)
    32U
Correct answer is option 'B'. Can you explain this answer?
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Explanation:

To understand why the correct answer is option 'B', let's look at the concept of potential energy stored in a spring.

1. Potential Energy in a Spring:
When a spring is stretched or compressed, it stores potential energy. This potential energy is given by the formula:

U = (1/2) * k * x^2

Where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

2. Given Information:
In this question, it is given that when the spring is stretched through 1 cm, it has a potential energy U. Let's denote this displacement as x1 = 1 cm.

We need to find the potential energy when the spring is stretched by 4 cm, which can be denoted as x2 = 4 cm.

3. Calculation:
Using the formula for potential energy in a spring, we can compare the potential energies at the two different displacements.

U1 = (1/2) * k * x1^2
U2 = (1/2) * k * x2^2

Substituting the given values:

U1 = (1/2) * k * (1 cm)^2
U2 = (1/2) * k * (4 cm)^2

Simplifying further:

U1 = (1/2) * k * 1 cm^2
U2 = (1/2) * k * 16 cm^2
U2 = 8 * (1/2) * k * 1 cm^2
U2 = 8 * U

Therefore, the potential energy when the spring is stretched by 4 cm is 8 times the potential energy when it is stretched by 1 cm. In other words, the potential energy becomes 8U.

Hence, the correct answer is option 'B' - 16U.
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Clockwork refers to the inner workings of mechanical clock or watch (where it is known as “movement”) and different types of toys which work using a series of gears driven by a spring. Clockwork device is completely mechanical and its essential parts are:• A key (or crown) which you wind to add energy• A spiral spring in which the energy is stored• A set of gears through which the spring's energy is released. The gears control how quickly (or slowly) a clockwork machine can do things. Such as in mechanical clock / watch the mechanism is the set of hands that sweep around the dial to tell the time. In a clockwork car toy, the gears drive the wheels.Winding the clockwork with the key means tightening a sturdy metal spring, called the mainspring. It is the process of storing potential energy. Clockwork springs are usually twists of thick steel, so tightening them (forcing the spring to occupy a much smaller spac e) is actually quite hard work. With each turn of the key, fingers do work and potential energy is stored in the spring. The amount of energy stored depends on the size and tension of the spring. Harder a spring is to turn and longer it is wound, the more energy it stores.While the spring uncoils, the potential energy is converted into kinetic energy through gears, cams, cranks and shafts which allow wheels to move faster or slower. In an ancient clock, gears transform the speed of a rotating shaft so that it drives the second hand at one speed, the minute hand at 1/60 that speed, and the hour hand at 1/3600 that speed. Clockwork toy cars often use gears to make themselves race along at surprising speed.When the spring of a clockwork uncoils

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A spring with spring constant k when stretched through 1 cm has a potential energy U. If it is stretched by 4 cm, the potential energy will becomea)4Ub)16Uc)8Ud)32UCorrect answer is option 'B'. Can you explain this answer?
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