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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times the time taken by it to reach the highest point of its path. The relation between H, u and n is:

1. 2gH = n²u²
2. gH = (n − 2)u²
3. 2gH = nu²(n − 2)
4. gH = (n − 2)u²

Correct answer: 2gH = nu²(n − 2)

Solution

The correct option relates the height of the tower, the initial velocity, and the time taken for the particle to reach the ground and its highest point. By analyzing the motion of the particle, we can derive that the total time of flight is proportional to the square of the initial velocity and the height, leading to the equation 2gH = nu²(n − 2), which accounts for the time ratios involved.

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