Problem Statement:
A packet of weight W is dropped with the help of a parachute and on striking the ground comes to rest with a retardation equal to twice the acceleration due to gravity. What is the force exerted on the ground?

Solution:

Given:
Weight of the packet, W

Retardation:
The packet comes to rest with a retardation equal to twice the acceleration due to gravity.

Acceleration due to Gravity:
The acceleration due to gravity is denoted by the symbol 'g'. In this case, the retardation is equal to twice the acceleration due to gravity, so the retardation is equal to 2g.

Force Exerted on the Ground:
To find the force exerted on the ground, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.

Steps to Calculate the Force Exerted on the Ground:

Step 1: Determine the mass of the packet
The weight of an object is equal to the mass of the object multiplied by the acceleration due to gravity. In this case, the weight of the packet is given as W, so we can write:

Weight = mass * acceleration due to gravity
W = mass * g

Step 2: Calculate the acceleration of the packet
The retardation of the packet is given as 2g. Since acceleration is the negative of retardation, we can write:

Acceleration = -2g

Step 3: Calculate the force exerted on the ground
Using Newton's second law of motion, we can write:

Force = mass * acceleration
Force = mass * (-2g)

Substituting the value of mass from Step 1, we get:

Force = (W/g) * (-2g)
Force = -2W

Therefore, the force exerted on the ground is equal to -2W.

Conclusion:
The force exerted on the ground when a packet of weight W is dropped with a parachute and comes to rest with a retardation equal to twice the acceleration due to gravity is -2W.