A 10m long chain of linear mass density 0.8kg/m is hanging freely from a rigid support.If g = 10m/sec^2 then power required to lift the chain up to the point of support 10 seconds is Explanation?

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Problem Statement:
A 10m long chain with a linear mass density of 0.8kg/m is hanging freely from a rigid support. The acceleration due to gravity is 10m/s^2. Determine the power required to lift the chain up to the point of support in 10 seconds.

Solution:
To find the power required to lift the chain, we need to calculate the work done in lifting the chain and divide it by the time taken.

Step 1: Calculate the mass of the chain:
The mass of the chain can be calculated using the linear mass density and the length of the chain.
Mass = Linear mass density × Length
Mass = 0.8kg/m × 10m
Mass = 8kg

Step 2: Calculate the work done:
The work done in lifting the chain is equal to the change in potential energy.
Work = Change in potential energy

The initial potential energy of the chain is zero as it is hanging freely. The final potential energy is determined by the height it is lifted. In this case, it is lifted to the same height as the support point.

Potential energy = Mass × gravitational acceleration × height

Since the height is not given, we assume it to be 10m (same as the length of the chain).

Potential energy = 8kg × 10m/s^2 × 10m
Potential energy = 800 Joules

Therefore, the work done in lifting the chain is 800 Joules.

Step 3: Calculate the power:
Power is defined as the rate at which work is done. Therefore, it is calculated by dividing the work done by the time taken.

Power = Work / Time

Power = 800 Joules / 10 seconds
Power = 80 Watts

Therefore, the power required to lift the chain up to the point of support in 10 seconds is 80 Watts.

Summary:
- The mass of the chain is 8kg.
- The work done in lifting the chain is 800 Joules.
- The power required to lift the chain in 10 seconds is 80 Watts.

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