A small airplane is sitting at rest on the ground. Its center of gravity is 2.58 m behind the nose of the airplane, the front wheel (nose wheel) is 0.800 m behind the nose, and the main wheels are 3.02 m behind the nose. What percentage of the airplane's weight is supported by the nose wheel?

The percentage of the weight supported by the front wheel is  A= 19.82 %

Explanation:

From the question we are told that

   The center of gravity of the plane to its nose  is  

    The distance of the front wheel of the plane to  its nose is

     The distance of the main wheel of the plane to its nose is

At equilibrium  the Torque about the nose of the airplane is mathematically represented as

Where m is the mass of the airplane

          is the weight of the airplane supported by the main wheel  

       So  

Substituting values

Now the weight supported at the frontal wheel is mathematically evaluated as

Substituting values      

Now the weight of the airplane is  =  mg

Thus percentage of this weight supported by the front wheel is   19.82 %