two 20g flatworms climb over a very thin obstruction 10 cm high .one of worm is 20cm long,the other is wider and only 10cm long.what is the ratio of amount of workdone by two worms ,when half of it is over the top of the wall?

To determine the ratio of the work done by the two flatworms as they climb over a 10 cm high obstruction, we first need to understand the concept of work in physics. Work is defined as the force applied to an object multiplied by the distance over which that force is applied. In this case, the force exerted by each worm is equal to its weight, which is the product of its mass and the acceleration due to gravity. Since both worms have the same mass of 20 grams, we can focus on how the dimensions of each worm affect the work done as they climb over the wall.

Understanding the Forces Involved

Each worm's weight can be calculated using the formula:

• Weight (W) = mass (m) × gravity (g)

Assuming the acceleration due to gravity (g) is approximately 9.81 m/s², the weight of each worm is:

• W = 0.02 kg × 9.81 m/s² = 0.1962 N

Calculating Work Done by Each Worm

When the worms climb over the obstruction, they need to exert a force equal to their weight to lift themselves against gravity. The work done (W) against gravity can be calculated using the formula:

• Work (W) = Force (F) × Distance (d)

In this scenario, the distance (d) is the height of the obstruction, which is 10 cm or 0.1 m. Therefore, the work done by each worm to climb over the wall is:

• W = 0.1962 N × 0.1 m = 0.01962 J

Considering the Length of the Worms

While the length of the worms (20 cm and 10 cm) might suggest that one worm has to exert more effort due to its size, the work done in lifting against gravity remains the same for both worms since they are both climbing the same height and have the same mass. The width of the worms does not affect the vertical work done, as work is dependent solely on the force exerted and the distance moved vertically.

Ratio of Work Done

Since both worms do the same amount of work to climb over the wall, the ratio of the work done by the two worms is:

• Ratio = Work done by Worm 1 : Work done by Worm 2 = 0.01962 J : 0.01962 J = 1 : 1

Conclusion

In summary, despite their differences in length, both flatworms perform the same amount of work to climb over the 10 cm obstruction. Therefore, the ratio of the work done by the two worms is 1:1. This illustrates an important principle in physics: when considering work done against gravity, the mass and height are the key factors, while the dimensions of the objects do not influence the work done in this context.