A body is trown vertically upward with velocity (u) , the greatest height to which will rise will be, (a) u/g, b) u²/2g, c) u²/g d) u/2g?

The correct answer is (b) u²/2g.

When a body is thrown vertically upward, the initial velocity is u and the acceleration due to gravity is g. The body will reach its maximum height when its final velocity becomes 0.

Using the equation of motion for vertical motion:
v² = u² + 2as

At the maximum height, the final velocity is 0, so:
0 = u² - 2gs

Rearranging the equation, we get:
2gs = u²

Therefore, the maximum height reached by the body is given by:
h = u²/2g

So, the correct answer is (b) u²/2g.

b) u²/2g