Two supports, made of the same material and initially of equal length, are 2.0 m apart. A stiff board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support at the left end and the other at the midpoint. A block is placed on the board a distance of 0.50 m from left end. As a result the board is horizontal (that is, the downward force on each support is the same). The mass of the block is:

20 kg

Explanation:

Assuming that the board remains horizontal with the unknown mass on it, then F = kx

If we add the vertical forces to zero, we have something like this

2F - (M + 10)g = 0

2F = (M + 10)g, next, divide both sides by 2

F = (M + 10)g/2

Since we were able to sum the moments at the right end of the board to zero, we then proceed to find the unknown mass M

To start, we say, Let the clockwise moment is positive, and so

F * 4 + F * 2 - Mg * 3.5 - 10 * g * 2 = 0

4F + 2F - 3.5Mg - 10 * 2 * g = 0

6F - 3.5Mg - 10 * 2 * g = 0,

Remember from above, we say that

F = M + 10)g/2, now, all we do is substitute it inside this equation

6 * (M + 10)g/2 - 3.5Mg - 10 * 2 * g = 0

3 * (M + 10)g - 3.5Mg - 10 * g * 2 = 0, divide all sides by g(so as to eliminate it)

3 (M + 10) - 3.5M - 10 * 2= 0

3M + 30 - 3.5M - 20 = 0

-0.5M + 10 = 0

0.5M = 10

M = 10/0.5

M = 20 kg

the answer is 3.1 his answer is wrong mines is right

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min