Question

A 10g mass placed on the pan of a spring balance causes an extension of 5cm. If a 15g mass is placed on the pan of the same spring balance, the extension is:

A) 3.3cm
B) 6.5cm
C) 0.5cm
D) 16.6cm
E) 15.0cm

Answer 1

The extension caused by a 15g mass on a spring balance that extends 5cm for a 10g mass would be 7.5cm, following the proportional relationship of Hooke's Law; however, this extension is not listed in the provided options.

Step-by-step explanation:

If a 10g mass causes a 5cm extension on a spring balance, we can use Hooke's Law to calculate the extension caused by a 15g mass. Hooke's Law states that Force (F) = k × Extension (x), where k is the spring constant and x is the extension of the spring. The force exerted by the mass is the weight of the mass, which is mass (m) multiplied by the acceleration due to gravity (g).

For the 10g mass, the force is 10g × 9.8 m/s2. The spring constant (k) can be calculated by rearranging the equation k = F/x. Once we have the spring constant, we can find the extension for a 15g mass using the same spring constant. Assuming the spring constant (k) remains constant, a linear relationship exists between the force and the extension.

For the 15g mass, the force will be 1.5 times the force of the 10g mass. Therefore, the extension will also be 1.5 times greater. So, the 15g mass will cause an extension of 7.5cm, which is not explicitly listed in the options provided, indicating a possible error in the options given.