A string is stretched by 2cm and its potential energy is u .if it is strechted by 10 cm,the potential energy is:
A.u\5
B.5u
C.10u
D.25u
To determine the potential energy when the string is stretched by 10 cm, we need to understand the relationship between potential energy and the amount of stretch in the string.
The potential energy of a stretched string is directly proportional to the square of the amount of stretch or displacement. This can be mathematically represented as:
Potential Energy ∝ (Amount of stretch)^2
Now, we are given that when the string is stretched by 2 cm, the potential energy is u. Using the relation mentioned above, we can formulate the equation:
u ∝ (2 cm)^2
Simplifying the equation, we have:
u ∝ 4 cm^2
Now, let's find the constant of proportionality by rearranging the equation:
u = k * 4 cm^2
Here, k represents the constant of proportionality. To determine the value of k, we need additional information. Luckily, we are given another point on the relationship. When the string is stretched by 10 cm, we need to find the potential energy.
Plugging this value into the equation, we have:
Potential Energy = k * (10 cm)^2
Potential Energy = k * 100 cm^2
Therefore, the potential energy when the string is stretched by 10 cm is proportional to 100 cm^2.
From the equation, we can observe that the potential energy has increased by a factor of 100/4 = 25.
So, the correct answer is option D. The potential energy is 25u when the string is stretched by 10 cm.